Pyleoclim Utilities API (pyleoclim.utils)
Utilities upon which Pyleoclim depends for higher-level functionalities accessible to users.
Pyleoclim makes extensive use of functions from numpy, Pandas, Scipy, Matplotlib, Statsmodels, and scikit-learn. Please note that some default parameter values for these functions have been changed to values more appropriate for paleoclimate datasets.
Causality
Utilities for Liang and Granger causality analysis
- pyleoclim.utils.causality.granger_causality(y1, y2, maxlag=1, addconst=True, verbose=True)[source]
Granger causality tests
Four tests for the Granger non-causality of 2 time series.
All four tests give similar results. params_ftest and ssr_ftest are equivalent based on F test which is identical to lmtest:grangertest in R.
Wrapper for the functions described in statsmodels (https://www.statsmodels.org/stable/generated/statsmodels.tsa.stattools.grangercausalitytests.html)
- Parameters
y1 (array) – vectors of (real) numbers with identical length, no NaNs allowed
y2 (array) – vectors of (real) numbers with identical length, no NaNs allowed
maxlag (int or int iterable, optional) – If an integer, computes the test for all lags up to maxlag. If an iterable, computes the tests only for the lags in maxlag.
addconst (bool, optional) – Include a constant in the model.
verbose (bool, optional) – Print results
- Returns
All test results, dictionary keys are the number of lags. For each lag the values are a tuple, with the first element a dictionary with test statistic, pvalues, degrees of freedom, the second element are the OLS estimation results for the restricted model, the unrestricted model and the restriction (contrast) matrix for the parameter f_test.
- Return type
dict
Notes
The null hypothesis for Granger causality tests is that y2, does NOT Granger cause y1. Granger causality means that past values of y2 have a statistically significant effect on the current value of y1, taking past values of y1 into account as regressors. We reject the null hypothesis that y2 does not Granger cause y1 if the p-values are below a desired threshold (e.g. 0.05).
The null hypothesis for all four test is that the coefficients corresponding to past values of the second time series are zero.
‘params_ftest’, ‘ssr_ftest’ are based on the F distribution
‘ssr_chi2test’, ‘lrtest’ are based on the chi-square distribution
See also
pyleoclim.utils.causality.liang_causality
information flow estimated using the Liang algorithm
pyleoclim.utils.causality.signif_isopersist
significance test with AR(1) with same persistence
pyleoclim.utils.causality.signif_isospec
significance test with surrogates with randomized phases
References
Granger, C. W. J. (1969). Investigating causal relations by econometric models and cross-spectral methods. Econometrica, 37(3), 424-438.
Granger, C. W. J. (1980). Testing for causality: A personal viewpoont. Journal of Economic Dynamics and Control, 2, 329-352.
Granger, C. W. J. (1988). Some recent development in a concept of causality. Journal of Econometrics, 39(1-2), 199-211.
- pyleoclim.utils.causality.liang(y1, y2, npt=1)[source]
Estimate the Liang information transfer from series y2 to series y1
- Parameters
y1 (array) – Vectors of (real) numbers with identical length, no NaNs allowed
y2 (array) – Vectors of (real) numbers with identical length, no NaNs allowed
npt (int >=1) – Time advance in performing Euler forward differencing, e.g., 1, 2. Unless the series are generated with a highly chaotic deterministic system, npt=1 should be used
- Returns
res –
A dictionary of results including:
- T21float
information flow from y2 to y1 (Note: not y1 -> y2!)
- tau21float
the standardized information flow from y2 to y1
- Zfloat
the total information flow from y2 to y1
- dH1_starfloat
dH*/dt (Liang, 2016)
dH1_noise : float
- Return type
dict
See also
pyleoclim.utils.causality.liang_causality
information flow estimated using the Liang algorithm
pyleoclim.utils.causality.granger_causality
information flow estimated using the Granger algorithm
pyleoclim.utils.causality.signif_isopersist
significance test with AR(1) with same persistence
pyleoclim.utils.causality.signif_isospec
significance test with surrogates with randomized phases
References
- Liang, X.S. (2013) The Liang-Kleeman Information Flow: Theory and
Applications. Entropy, 15, 327-360, doi:10.3390/e15010327
- Liang, X.S. (2014) Unraveling the cause-effect relation between timeseries.
Physical review, E 90, 052150
- Liang, X.S. (2015) Normalizing the causality between time series.
Physical review, E 92, 022126
- Liang, X.S. (2016) Information flow and causality as rigorous notions ab initio.
Physical review, E 94, 052201
- pyleoclim.utils.causality.liang_causality(y1, y2, npt=1, signif_test='isospec', nsim=1000, qs=[0.005, 0.025, 0.05, 0.95, 0.975, 0.995])[source]
Liang-Kleeman information flow
Estimate the Liang information transfer from series y2 to series y1 with significance estimates using either an AR(1) tests with series with the same persistence or surrogates with randomized phases.
- Parameters
y1 (array) – vectors of (real) numbers with identical length, no NaNs allowed
y2 (array) – vectors of (real) numbers with identical length, no NaNs allowed
npt (int >=1) – time advance in performing Euler forward differencing, e.g., 1, 2. Unless the series are generated with a highly chaotic deterministic system, npt=1 should be used
signif_test (str; {'isopersist', 'isospec'}) – the method for significance test see signif_isospec and signif_isopersist for details.
nsim (int) – the number of AR(1) surrogates for significance test
qs (list) – the quantiles for significance test
- Returns
res –
A dictionary of results including:
- T21float
information flow from y2 to y1 (Note: not y1 -> y2!)
- tau21float
the standardized information flow from y2 to y1
- Zfloat
the total information flow from y2 to y1
- dH1_starfloat
dH*/dt (Liang, 2016)
dH1_noise : float
- signif_qs :
the quantiles for significance test
- T21_noiselist
the quantiles of the information flow from noise2 to noise1 for significance testing
- tau21_noiselist
the quantiles of the standardized information flow from noise2 to noise1 for significance testing
- Return type
dict
See also
pyleoclim.utils.causality.liang
information flow estimated using the Liang algorithm
pyleoclim.utils.causality.granger_causality
information flow estimated using the Granger algorithm
pyleoclim.utils.causality.signif_isopersist
significance test with AR(1) with same persistence
pyleoclim.utils.causality.causality.signif_isospec
significance test with surrogates with randomized phases
References
Liang, X.S. (2013) The Liang-Kleeman Information Flow: Theory and Applications. Entropy, 15, 327-360, doi:10.3390/e15010327
Liang, X.S. (2014) Unraveling the cause-effect relation between timeseries. Physical review, E 90, 052150
Liang, X.S. (2015) Normalizing the causality between time series. Physical review, E 92, 022126
Liang, X.S. (2016) Information flow and causality as rigorous notions ab initio. Physical review, E 94, 052201
- pyleoclim.utils.causality.signif_isopersist(y1, y2, method, nsim=1000, qs=[0.005, 0.025, 0.05, 0.95, 0.975, 0.995], **kwargs)[source]
significance test with AR(1) with same persistence
- Parameters
y1 (array) – vectors of (real) numbers with identical length, no NaNs allowed
y2 (array) – vectors of (real) numbers with identical length, no NaNs allowed
method (str; {'liang'}) – estimates for the Liang method
nsim (int) – the number of AR(1) surrogates for significance test
qs (list) – the quantiles for significance test
- Returns
res_dict –
A dictionary with the following information:
T21_noise_qs : list the quantiles of the information flow from noise2 to noise1 for significance testing
tau21_noise_qs : list the quantiles of the standardized information flow from noise2 to noise1 for significance testing
- Return type
dict
See also
pyleoclim.utils.causality.liang_causality
information flow estimated using the Liang algorithm
pyleoclim.utils.causality.granger_causality
information flow estimated using the Granger algorithm
pyleoclim.utils.causality.signif_isospec
significance test with surrogates with randomized phases
- pyleoclim.utils.causality.signif_isospec(y1, y2, method, nsim=1000, qs=[0.005, 0.025, 0.05, 0.95, 0.975, 0.995], **kwargs)[source]
significance test with surrogates with randomized phases
- Parameters
y1 (array) – vectors of (real) numbers with identical length, no NaNs allowed
y2 (array) – vectors of (real) numbers with identical length, no NaNs allowed
method (str; {'liang'}) – estimates for the Liang method
nsim (int) – the number of surrogates for significance test
qs (list) – the quantiles for significance test
kwargs (dict) – keyword arguments for the causality method (e.g. npt for Liang-Kleeman)
- Returns
res_dict –
A dictionary with the following information:
- T21_noise_qslist
the quantiles of the information flow from noise2 to noise1 for significance testing
- tau21_noise_qslist
the quantiles of the standardized information flow from noise2 to noise1 for significance testing
- Return type
dict
See also
pyleoclim.utils.causality.liang_causality
information flow estimated using the Liang algorithm
pyleoclim.utils.causality.granger_causality
information flow estimated using the Granger algorithm
pyleoclim.utils.causality.signif_isopersist
significance test with AR(1) with same persistence
Correlation
Relevant functions for correlation analysis
- pyleoclim.utils.correlation.corr_isopersist(y1, y2, alpha=0.05, nsim=1000)[source]
Computes the Pearson’s correlation between two timeseries, and their significance using Ar(1) modeling.
The significance is gauged via a non-parametric (Monte Carlo) simulation of correlations with nsim AR(1) processes with identical persistence properties as x and y ; the measure of which is the lag-1 autocorrelation (g).
- Parameters
y1 (array) – vectors of (real) numbers with identical length, no NaNs allowed
y2 (array) – vectors of (real) numbers with identical length, no NaNs allowed
alpha (float) – significance level for critical value estimation [default: 0.05]
nsim (int) – number of simulations [default: 1000]
- Returns
r (float) – correlation between x and y
signif (bool) – true (1) if significant; false (0) otherwise
pval (float) – test p-value (the probability of the test statstic exceeding the observed one by chance alone)
Notes
The probability of obtaining a test statistic at least as extreme as the one actually observed, assuming that the null hypothesis is true. The test is 1 tailed on |r|: Ho = { |r| = 0 }, Ha = { |r| > 0 } The test is rejected (signif = 1) if pval <= alpha, otherwise signif=0; (Some Rights Reserved) Hepta Technologies, 2009 v1.0 USC, Aug 10 2012, based on corr_signif.
See also
pyleoclim.utils.correlation.corr_sig
Estimates the Pearson’s correlation and associated significance between two non IID time series
pyleoclim.utils.correlation.corr_ttest
Estimates Pearson’s correlation and associated significance using a t-test
pyleoclim.utils.correlation.corr_isospec
Estimates Pearson’s correlation and associated significance using
pyleoclim.utils.correlation.fdr
Determine significance based on the false discovery rate
- pyleoclim.utils.correlation.corr_isospec(y1, y2, alpha=0.05, nsim=1000)[source]
Estimates the significance of the correlation using phase randomization
Estimates the significance of correlations between non IID time series by phase randomization of original inputs. This function creates ‘nsim’ random time series that have the same power spectrum as the original time series but random phases.
- Parameters
y1 (array) – vectors of (real) numbers with identical length, no NaNs allowed
y2 (array) – vectors of (real) numbers with identical length, no NaNs allowed
alpha (float) – significance level for critical value estimation [default: 0.05]
nsim (int) – number of simulations [default: 1000]
- Returns
r (float) – correlation between y1 and y2
signif (bool) – true (1) if significant; false (0) otherwise
F (float) – Fraction of time series with higher correlation coefficents than observed (approximates the p-value).
See also
pyleoclim.utils.correlation.corr_sig
Estimates the Pearson’s correlation and associated significance between two non IID time series
pyleoclim.utils.correlation.corr_ttest
Estimates Pearson’s correlation and associated significance using a t-test
pyleoclim.utils.correlation.corr_isopersist
Estimates Pearson’s correlation and associated significance using AR(1) simulations
pyleoclim.utils.correlation.fdr
Determine significance based on the false discovery rate
References
Ebisuzaki, W, 1997: A method to estimate the statistical significance of a correlation when the data are serially correlated. J. of Climate, 10, 2147-2153.
Prichard, D., Theiler, J. Generating Surrogate Data for Time Series with Several Simultaneously Measured Variables (1994) Physical Review Letters, Vol 73, Number 7 (Some Rights Reserved) USC Climate Dynamics Lab, 2012.
- pyleoclim.utils.correlation.corr_sig(y1, y2, nsim=1000, method='isospectral', alpha=0.05)[source]
Estimates the Pearson’s correlation and associated significance between two non IID time series
The significance of the correlation is assessed using one of the following methods:
- ‘ttest’: T-test adjusted for effective sample size.
This is a parametric test (data are Gaussian and identically distributed) with a rather ad-hoc adjustment. It is instantaneous but makes a lot of assumptions about the data, many of which may not be met.
- ‘isopersistent’: AR(1) modeling of x and y.
This is a parametric test as well (series follow an AR(1) model) but solves the issue by direct simulation.
- ‘isospectral’: phase randomization of original inputs. (default)
This is a non-parametric method, assuming only wide-sense stationarity
For 2 and 3, computational requirements scale with nsim. When possible, nsim should be at least 1000.
- Parameters
y1 (array) – vector of (real) numbers of same length as y2, no NaNs allowed
y2 (array) – vector of (real) numbers of same length as y1, no NaNs allowed
nsim (int) – the number of simulations [default: 1000]
method (str; {'ttest','isopersistent','isospectral' (default)}) – method for significance testing
alpha (float) – significance level for critical value estimation [default: 0.05]
- Returns
res – the result dictionary, containing
- rfloat
correlation coefficient
- pfloat
the p-value
- signifbool
true if significant; false otherwise Note that signif = True if and only if p <= alpha.
- Return type
dict
See also
pyleoclim.utils.correlation.corr_ttest
Estimates the significance of correlations between 2 time series using the classical T-test adjusted for effective sample size
pyleoclim.utils.correlation.corr_isopersist
Computes correlation between two timeseries, and their significance using Ar(1) modeling
pyleoclim.utils.correlation.corr_isospec
Estimates the significance of the correlation using phase randomization
pyleoclim.utils.correlation.fdr
Determine significance based on the false discovery rate
- pyleoclim.utils.correlation.corr_ttest(y1, y2, alpha=0.05)[source]
Estimates the significance of correlations between 2 time series using the classical T-test adjusted for effective sample size.
The degrees of freedom are adjusted following n_eff=n(1-g)/(1+g) where g is the lag-1 autocorrelation.
- Parameters
y1 (array) – vectors of (real) numbers with identical length, no NaNs allowed
y2 (array) – vectors of (real) numbers with identical length, no NaNs allowed
alpha (float) – significance level for critical value estimation [default: 0.05]
- Returns
r (float) – correlation between x and y
signif (bool) – true (1) if significant; false (0) otherwise
pval (float) – test p-value (the probability of the test statistic exceeding the observed one by chance alone)
See also
pyleoclim.utils.correlation.corr_sig
Estimates the Pearson’s correlation and associated significance between two non IID time series
pyleoclim.utils.correlation.corr_isopersist
Estimate Pearson’s correlation and associated significance using AR(1)
pyleoclim.utils.correlation.corr_isospec
Estimate Pearson’s correlation and associated significance using phase randomization
pyleoclim.utils.correlation.fdr
Determine significance based on the false discovery rate
- pyleoclim.utils.correlation.cov_shrink_rblw(S, n)[source]
Compute a shrinkage estimate of the covariance matrix using the Rao-Blackwellized Ledoit-Wolf estimator described by Chen et al. 2011 [1]
Contributed by Robert McGibbon.
- Parameters
S (array, shape=(n, n)) – Sample covariance matrix (e.g. estimated with np.cov(X.T))
n (int) – Number of data points used in the estimate of S.
- Returns
sigma (array, shape=(p, p)) – Estimated shrunk covariance matrix
shrinkage (float) – The applied covariance shrinkage intensity.
Notes
See the covar documentation for math details.
References
Chen, A. Wiesel and A. O. Hero (2011), Robust Shrinkage Estimation of High-Dimensional Covariance Matrices, IEEE Transactions on Signal Processing, vol. 59, no. 9, pp. 4097-4107, doi:10.1109/TSP.2011.2138698
See also
sklearn.covariance.ledoit_wolf
very similar approach using the same shrinkage target, \(T\), but a different method for estimating the shrinkage intensity, \(gamma\).
- pyleoclim.utils.correlation.fdr(pvals, qlevel=0.05, method='original', adj_method=None, adj_args={})[source]
Determine significance based on the false discovery rate
The false discovery rate is a method of conceptualizing the rate of type I errors in null hypothesis testing when conducting multiple comparisons. Translated from fdr.R by Dr. Chris Paciorek
- Parameters
pvals (list or array) – A vector of p-values on which to conduct the multiple testing.
qlevel (float) – The proportion of false positives desired.
method ({'original', 'general'}) –
Method for performing the testing.
’original’ follows Benjamini & Hochberg (1995);
’general’ is much more conservative, requiring no assumptions on the p-values (see Benjamini & Yekutieli (2001)).
’original’ is recommended, and if desired, using ‘adj_method=”mean”’ to increase power.
adj_method ({'mean', 'storey', 'two-stage'}) –
Method for increasing the power of the procedure by estimating the proportion of alternative p-values.
’mean’, the modified Storey estimator in Ventura et al. (2004)
’storey’, the method of Storey (2002)
’two-stage’, the iterative approach of Benjamini et al. (2001)
adj_args (dict) – Arguments for adj_method; see prop_alt() for description, but note that for “two-stage”, qlevel and fdr_method are taken from the qlevel and method arguments for fdr()
- Returns
fdr_res – A vector of the indices of the significant tests; None if no significant tests
- Return type
array or None
See also
pyleoclim.utils.correlation.corr_sig
Estimates the Pearson’s correlation and associated significance between two non IID time series
References
fdr.R by Dr. Chris Paciorek: https://www.stat.berkeley.edu/~paciorek/research/code/code.html
- pyleoclim.utils.correlation.fdr_basic(pvals, qlevel=0.05)[source]
The basic FDR of Benjamini & Hochberg (1995).
- Parameters
pvals (list or array) – A vector of p-values on which to conduct the multiple testing.
qlevel (float) – The proportion of false positives desired.
- Returns
fdr_res – A vector of the indices of the significant tests; None if no significant tests
- Return type
array or None
See also
pyleoclim.utils.correlation.corr_sig
Estimates the Pearson’s correlation and associated significance between two non IID time series
pyleoclim.utils.correlation.fdf
Determine significance based on the false discovery rate
References
Benjamini, Yoav; Hochberg, Yosef (1995). “Controlling the false discovery rate: a practical and powerful approach to multiple testing”. Journal of the Royal Statistical Society, Series B. 57 (1): 289–300. MR 1325392
- pyleoclim.utils.correlation.fdr_master(pvals, qlevel=0.05, method='original')[source]
Perform various versions of the FDR procedure
- Parameters
pvals (list or array) – A vector of p-values on which to conduct the multiple testing.
qlevel (float) – The proportion of false positives desired.
method ({'original', 'general'}) – Method for performing the testing. - ‘original’ follows Benjamini & Hochberg (1995); - ‘general’ is much more conservative, requiring no assumptions on the p-values (see Benjamini & Yekutieli (2001)). We recommend using ‘original’, and if desired, using ‘adj_method=”mean”’ to increase power.
- Returns
fdr_res – A vector of the indices of the significant tests; None if no significant tests
- Return type
array or None
See also
pyleoclim.utils.correlation.corr_sig
Estimates the Pearson’s correlation and associated significance between two non IID time series
pyleoclim.utils.correlation.fdf
Determine significance based on the false discovery rate
References
Benjamini, Yoav; Hochberg, Yosef (1995). “Controlling the false discovery rate: a practical and powerful approach to multiple testing”. Journal of the Royal Statistical Society, Series B. 57 (1): 289–300. MR 1325392
Benjamini, Yoav; Yekutieli, Daniel (2001). “The control of the false discovery rate in multiple testing under dependency”. Annals of Statistics. 29 (4): 1165–1188. doi:10.1214/aos/1013699998
- pyleoclim.utils.correlation.isopersistent_rn(X, p)[source]
Generates p realization of a red noise [i.e. AR(1)] process with same persistence properties as X (Mean and variance are also preserved).
- Parameters
X (array) – vector of (real) numbers as a time series, no NaNs allowed
p (int) – number of simulations
- Returns
red (numpy array) – n rows by p columns matrix of an AR1 process, where n is the size of X
g (float) – lag-1 autocorrelation coefficient
See also
pyleoclim.utils.correlation.corr_sig
Estimates the Pearson’s correlation and associated significance between two non IID time series
pyleoclim.utils.correlation.fdr
Determine significance based on the false discovery rate
Notes
(Some Rights Reserved) Hepta Technologies, 2008
- pyleoclim.utils.correlation.phaseran(recblk, nsurr)[source]
Simultaneous phase randomization of a set of time series
It creates blocks of surrogate data with the same second order properties as the original time series dataset by transforming the oriinal data into the frequency domain, randomizing the phases simultaneoulsy across the time series and converting the data back into the time domain.
Written by Carlos Gias for MATLAB
http://www.mathworks.nl/matlabcentral/fileexchange/32621-phase-randomization/content/phaseran.m
- Parameters
recblk (numpy array) – 2D array , Row: time sample. Column: recording. An odd number of time samples (height) is expected. If that is not the case, recblock is reduced by 1 sample before the surrogate data is created. The class must be double and it must be nonsparse.
nsurr (int) – is the number of image block surrogates that you want to generate.
- Returns
surrblk – 3D multidimensional array image block with the surrogate datasets along the third dimension
- Return type
numpy array
See also
pyleoclim.utils.correlation.corr_sig
Estimates the Pearson’s correlation and associated significance between two non IID time series
pyleoclim.utils.correlation.fdf
Determine significance based on the false discovery rate
References
Prichard, D., Theiler, J. Generating Surrogate Data for Time Series with Several Simultaneously Measured Variables (1994) Physical Review Letters, Vol 73, Number 7
Carlos Gias (2020). Phase randomization, MATLAB Central File Exchange
- pyleoclim.utils.correlation.prop_alt(pvals, adj_method='mean', adj_args={'edf_lower': 0.8, 'num_steps': 20})[source]
Calculate an estimate of a, the proportion of alternative hypotheses, using one of several methods
- Parameters
pvals (list or array) – A vector of p-values on which to estimate a
- adj_method: str; {‘mean’, ‘storey’, ‘two-stage’}
Method for increasing the power of the procedure by estimating the proportion of alternative p-values. - ‘mean’, the modified Storey estimator that we suggest in Ventura et al. (2004) - ‘storey’, the method of Storey (2002) - ‘two-stage’, the iterative approach of Benjamini et al. (2001)
- adj_argsdict
for “mean”, specify “edf_lower”, the smallest quantile at which to estimate a, and “num_steps”, the number of quantiles to use the approach uses the average of the Storey (2002) estimator for the num_steps quantiles starting at “edf_lower” and finishing just less than 1
for “storey”, specify “edf_quantile”, the quantile at which to calculate the estimator
for “two-stage”, the method uses a standard FDR approach to estimate which p-values are significant this number is the estimate of a; therefore the method requires specification of qlevel, the proportion of false positives and “fdr_method” (‘original’ or ‘general’), the FDR method to be used. We do not recommend ‘general’ as this is very conservative and will underestimate a.
- Returns
a – estimate of a, the number of alternative hypotheses
- Return type
int
See also
pyleoclim.utils.correlation.corr_sig
Estimates the Pearson’s correlation and associated significance between two non IID time series
pyleoclim.utils.correlation.fdf
Determine significance based on the false discovery rate
References
Storey, J.D. (2002). A direct approach to False Discovery Rates. Journal of the Royal Statistical Society, Series B, 64, 3, 479-498
Benjamini, Yoav; Yekutieli, Daniel (2001). “The control of the false discovery rate in multiple testing under dependency”. Annals of Statistics. 29 (4): 1165–1188. doi:10.1214/aos/1013699998
Ventura, V., Paciorek, C., Risbey, J.S. (2004). Controlling the proportion of falsely rejected hypotheses when conducting multiple tests with climatological data. Journal of climate, 17, 4343-4356
- pyleoclim.utils.correlation.sm_ar1_sim(n, p, g, sig)[source]
Produce p realizations of an AR1 process of length n with lag-1 autocorrelation g using statsmodels
- Parameters
n (int) – row dimensions
p (int) – column dimensions
g (float) – lag-1 autocorrelation coefficient
sig (float) – the standard deviation of the original time series
- Returns
red – n rows by p columns matrix of an AR1 process
- Return type
numpy matrix
See also
pyleoclim.utils.correlation.corr_sig
Estimates the Pearson’s correlation and associated significance between two non IID time series
pyleoclim.utils.correlation.fdr
Determine significance based on the false discovery rate
- pyleoclim.utils.correlation.storey(edf_quantile, pvals)[source]
The basic Storey (2002) estimator of a, the proportion of alternative hypotheses.
- Parameters
edf_quantile (float) – The quantile of the empirical distribution function at which to estimate a.
pvals (list or array) – A vector of p-values on which to estimate a
- Returns
a – estimate of a, the number of alternative hypotheses
- Return type
int
See also
pyleoclim.utils.correlation.corr_sig
Estimates the Pearson’s correlation and associated significance between two non IID time series
pyleoclim.utils.correlation.fdf
Determine significance based on the false discovery rate
References
Storey, J.D., 2002, A direct approach to False Discovery Rates. Journal of the Royal Statistical Society, Series B, 64, 3, 479-498
Decomposition
Eigendecomposition methods: Singular Spectrum Analysis (SSA). soon: PCA, Monte-Carlo PCA, Multi-Channel SSA
- pyleoclim.utils.decomposition.ssa(y, M=None, nMC=0, f=0.5, trunc=None, var_thresh=80, online=True)[source]
Singular spectrum analysis
Nonparametric eigendecomposition of timeseries into orthogonal oscillations. This implementation uses the method of [1], with applications presented in [2]. Optionally (nMC>0), the significance of eigenvalues is assessed by Monte-Carlo simulations of an AR(1) model fit to X, using [3]. The method expects regular spacing, but is tolerant to missing values, up to a fraction 0<f<1 (see [4]).
- Parameters
y (array of length N) – time series (evenly-spaced, possibly with up to f*N NaNs)
M (int) – window size (default: 10% of N)
nMC (int) – Number of iterations in the Monte-Carlo simulation (default nMC=0, bypasses Monte Carlo SSA) Currently only supported for evenly-spaced, gap-free data.
f (float) – maximum allowable fraction of missing values. (Default is 0.5)
trunc (str) –
- if present, truncates the expansion to a level K < M owing to one of 4 criteria:
’kaiser’: variant of the Kaiser-Guttman rule, retaining eigenvalues larger than the median
’mcssa’: Monte-Carlo SSA (use modes above the 95% quantile from an AR(1) process)
’var’: first K modes that explain at least var_thresh % of the variance.
- Default is None, which bypasses truncation (K = M)
’knee’: Wherever the “knee” of the screeplot occurs.
Recommended as a first pass at identifying significant modes as it tends to be more robust than ‘kaiser’ or ‘var’, and faster than ‘mcssa’. While no truncation method is imposed by default, if the goal is to enhance the S/N ratio and reconstruct a smooth version of the attractor’s skeleton, then the knee-finding method is a good compromise between objectivity and efficiency. See kneed’s documentation for more details on the knee finding algorithm.
var_thresh (float) – variance threshold for reconstruction (only impactful if trunc is set to ‘var’)
online (bool; {True,False}) –
Whether or not to conduct knee finding analysis online or offline. Only called when trunc = ‘knee’. Default is True See kneed’s documentation for details.
- Returns
res –
eigvals : (M, ) array of eigenvalues
eigvecs : (M, M) Matrix of temporal eigenvectors (T-EOFs)
PC : (N - M + 1, M) array of principal components (T-PCs)
RCmat : (N, M) array of reconstructed components
RCseries : (N,) reconstructed series, with mean and variance restored
pctvar: (M, ) array of the fraction of variance (%) associated with each mode
eigvals_q : (M, 2) array containting the 5% and 95% quantiles of the Monte-Carlo eigenvalue spectrum [ if nMC >0 ]
mode_idx : array of indices of eigenvalues >=eigvals_q
- Return type
dict containing:
References
[1]_ Vautard, R., and M. Ghil (1989), Singular spectrum analysis in nonlinear dynamics, with applications to paleoclimatic time series, Physica D, 35, 395–424.
[2]_ Ghil, M., R. M. Allen, M. D. Dettinger, K. Ide, D. Kondrashov, M. E. Mann, A. Robertson, A. Saunders, Y. Tian, F. Varadi, and P. Yiou (2002), Advanced spectral methods for climatic time series, Rev. Geophys., 40(1), 1003–1052, doi:10.1029/2000RG000092.
[3]_ Allen, M. R., and L. A. Smith (1996), Monte Carlo SSA: Detecting irregular oscillations in the presence of coloured noise, J. Clim., 9, 3373–3404.
[4]_ Schoellhamer, D. H. (2001), Singular spectrum analysis for time series with missing data, Geophysical Research Letters, 28(16), 3187–3190, doi:10.1029/2000GL012698.
See also
pyleoclim.core.series.Series.ssa
Singular Spectrum Analysis for timeseries objects
pyleoclim.core.ssares.SsaRes.modeplot
plot SSA modes
pyleoclim.core.ssares.SsaRes.screeplot
plot SSA eigenvalue spectrum
Filter
Utilities to filter arrayed timeseries data, leveraging SciPy
- pyleoclim.utils.filter.butterworth(ys, fc, fs=1, filter_order=3, pad='reflect', reflect_type='odd', params=(1, 0, 0), padFrac=0.1)[source]
- Applies a Butterworth filter with frequency fc, with padding
Supports both lowpass and band-pass filtering.
- Parameters
ys (numpy array) – Timeseries
fc (float or list) – cutoff frequency. If scalar, it is interpreted as a low-frequency cutoff (lowpass) If fc is a list, it is interpreted as a frequency band (f1, f2), with f1 < f2 (bandpass)
fs (float) – sampling frequency
filter_order (int) – order n of Butterworth filter
pad (str) –
Indicates if padding is needed.
’reflect’: Reflects the timeseries
’ARIMA’: Uses an ARIMA model for the padding
None: No padding.
params (tuple) – model parameters for ARIMA model (if pad = ‘ARIMA’)
padFrac (float) – fraction of the series to be padded
- Returns
yf – filtered array
- Return type
array
See also
pyleoclim.utils.filter.ts_pad
Pad a timeseries based on timeseries model predictions
pyleoclim.utils.filter.firwin
Applies a Finite Impulse Response filter with frequency fc, with padding
pyleoclim.utils.filter.savitzky_golay
Smooth (and optionally differentiate) data with a Savitzky-Golay filter
pyleoclim.utils.filter.lanczos
Applies a Lanczos filter with frequency fc, with padding
- pyleoclim.utils.filter.firwin(ys, fc, numtaps=None, fs=1, pad='reflect', window='hamming', reflect_type='odd', params=(1, 0, 0), padFrac=0.1, **kwargs)[source]
Applies a Finite Impulse Response filter design with window method and frequency fc, with padding
- Parameters
ys (numpy array) – Timeseries
fc (float or list) – cutoff frequency. If scalar, it is interpreted as a low-frequency cutoff (lowpass) If fc is a list, it is interpreted as a frequency band (f1, f2), with f1 < f2 (bandpass)
numptaps (int) – Length of the filter (number of coefficients, i.e. the filter order + 1). numtaps must be odd if a passband includes the Nyquist frequency. If None, will use the largest number that is smaller than 1/3 of the the data length.
fs (float) – sampling frequency
window (str or tuple of string and parameter values, optional) – Desired window to use. See scipy.signal.get_window for a list of windows and required parameters.
pad (str) –
Indicates if padding is needed.
’reflect’: Reflects the timeseries
’ARIMA’: Uses an ARIMA model for the padding
None: No padding.
params (tuple) – model parameters for ARIMA model (if pad = True)
padFrac (float) – fraction of the series to be padded
kwargs (dict) – a dictionary of keyword arguments for scipy.signal.firwin
- Returns
yf – filtered array
- Return type
array
See also
scipy.signal.firwin
FIR filter design using the window method
pyleoclim.utils.filter.ts_pad
Pad a timeseries based on timeseries model predictions
pyleoclim.utils.filter.butterworth
Applies a Butterworth filter with frequency fc, with padding
pyleoclim.utils.filter.lanczos
Applies a Lanczos filter with frequency fc, with padding
pyleoclim.utils.filter.savitzky_golay
Smooth (and optionally differentiate) data with a Savitzky-Golay filter
- pyleoclim.utils.filter.lanczos(ys, fc, fs=1, pad='reflect', reflect_type='odd', params=(1, 0, 0), padFrac=0.1)[source]
Applies a Lanczos (lowpass) filter with frequency fc, with optional padding
- Parameters
ys (numpy array) – Timeseries
fc (float) – cutoff frequency
fs (float) – sampling frequency
pad (str) –
Indicates if padding is needed
’reflect’: Reflects the timeseries
’ARIMA’: Uses an ARIMA model for the padding
None: No padding
params (tuple) – model parameters for ARIMA model (if pad = ‘ARIMA’). May require fiddling
padFrac (float) – fraction of the series to be padded
- Returns
yf – filtered array
- Return type
array
See also
pyleoclim.utils.filter.ts_pad
Pad a timeseries based on timeseries model predictions
pyleoclim.utils.filter.butterworth
Applies a Butterworth filter with frequency fc, with padding
pyleoclim.utils.filter.firwin
Applies a Finite Impulse Response filter with frequency fc, with padding
pyleoclim.utils.filter.savitzky_golay
Smooth (and optionally differentiate) data with a Savitzky-Golay filter
References
Filter design from http://scitools.org.uk/iris/docs/v1.2/examples/graphics/SOI_filtering.html
- pyleoclim.utils.filter.savitzky_golay(ys, window_length=None, polyorder=2, deriv=0, delta=1, axis=-1, mode='mirror', cval=0)[source]
Smooth (and optionally differentiate) data with a Savitzky-Golay filter.
The Savitzky-Golay filter removes high frequency noise from data. It has the advantage of preserving the original shape and features of the signal better than other types of filtering approaches, such as moving averages techniques.
The Savitzky-Golay is a type of low-pass filter, particularly suited for smoothing noisy data. The main idea behind this approach is to make for each point a least-square fit with a polynomial of high order over a odd-sized window centered at the point.
Uses the implementation from scipy.signal: https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.savgol_filter.html
- Parameters
ys (array) – the values of the signal to be filtered
window_length (int) – The length of the filter window. Must be a positive integer. If mode is ‘interp’, window_length must be less than or equal to the size of ys. Default is the size of ys.
polyorder (int) – The order of the polynomial used to fit the samples. polyorder Must be less than window_length. Default is 2
deriv (int) – The order of the derivative to compute. This must be a nonnegative integer. The default is 0, which means to filter the data without differentiating
delta (float) – The spacing of the samples to which the filter will be applied. This is only used if deriv>0. Default is 1.0
axis (int) – The axis of the array ys along which the filter will be applied. Default is -1
mode (str) – Must be ‘mirror’ (the default), ‘constant’, ‘nearest’, ‘wrap’ or ‘interp’. This determines the type of extension to use for the padded signal to which the filter is applied. When mode is ‘constant’, the padding value is given by cval. See the Notes for more details on ‘mirror’, ‘constant’, ‘wrap’, and ‘nearest’. When the ‘interp’ mode is selected, no extension is used. Instead, a degree polyorder polynomial is fit to the last window_length values of the edges, and this polynomial is used to evaluate the last window_length // 2 output values.
cval (scalar) – Value to fill past the edges of the input if mode is ‘constant’. Default is 0.0.
- Returns
yf – ndarray of shape (N), the smoothed signal (or its n-th derivative).
- Return type
array
See also
pyleoclim.utils.filter.butterworth
Applies a Butterworth filter with frequency fc, with padding
pyleoclim.utils.filter.lanczos
Applies a Lanczos filter with frequency fc, with padding
pyleoclim.utils.filter.firwin
Applies a Finite Impulse Response filter with frequency fc, with padding
References
Savitzky, M. J. E. Golay, Smoothing and Differentiation of Data by Simplified Least Squares Procedures. Analytical Chemistry, 1964, 36 (8), pp 1627-1639.
Numerical Recipes 3rd Edition: The Art of Scientific Computing W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery Cambridge University Press ISBN-13: 9780521880688
Notes
Details on the mode option:
‘mirror’: Repeats the values at the edges in reverse order. The value closest to the edge is not included.
‘nearest’: The extension contains the nearest input value.
‘constant’: The extension contains the value given by the cval argument.
‘wrap’: The extension contains the values from the other end of the array.
- pyleoclim.utils.filter.ts_pad(ys, ts, method='reflect', params=(1, 0, 0), reflect_type='odd', padFrac=0.1)[source]
Pad a timeseries based on timeseries model predictions
- Parameters
ys (numpy array) – Evenly-spaced timeseries
ts (numpy array) – Time axis
method (str) –
the method to use to pad the series
ARIMA: uses a fitted ARIMA model
reflect (default): Reflects the time series around either end.
params (tuple) – the ARIMA model order parameters (p,d,q), Default corresponds to an AR(1) model
reflect_type (str; {‘even’, ‘odd’}, optional) – Used in ‘reflect’, and ‘symmetric’. The ‘even’ style is the default with an unaltered reflection around the edge value. For the ‘odd’ style, the extented part of the array is created by subtracting the reflected values from two times the edge value. For more details, see np.lib.pad()
padFrac (float) – padding fraction (scalar) such that padLength = padFrac*length(series)
- Returns
yp (array) – padded timeseries
tp (array) – augmented time axis
See also
pyleoclim.utils.filter.butterworth
Applies a Butterworth filter with frequency fc, with padding
pyleoclim.utils.filter.lanczos
Applies a Lanczos filter with frequency fc, with padding
pyleoclim.utils.filter.firwin
Applies a Finite Impulse Response filter with frequency fc, with padding
Mapping
Mapping utilities for geolocated objects, leveraging Cartopy.
- pyleoclim.utils.mapping.compute_dist(lat_r, lon_r, lat_c, lon_c)[source]
Computes the distance in (km) between a reference point and an array of other coordinates.
- Parameters
lat_r (float) – The reference latitude, in deg
lon_r (float) – The reference longitude, in deg
lat_c (list) – A list of latitudes for the comparison points, in deg
lon_c (list) – A list of longitudes for the comparison points, in deg
See also
pyleoclim.utils.mapping.dist_sphere
calculate distance on a sphere
- Returns
dist – A list of distances in km.
- Return type
list
- pyleoclim.utils.mapping.dist_sphere(lat1, lon1, lat2, lon2)[source]
Uses the haversine formula to calculate distance on a sphere https://en.wikipedia.org/wiki/Haversine_formula
- Parameters
lat1 (float) – Latitude of the first point, in radians
lon1 (float) – Longitude of the first point, in radians
lat2 (float) – Latitude of the second point, in radians
lon2 (float) – Longitude of the second point, in radians
- Returns
dist – The distance between the two point in km
- Return type
float
- pyleoclim.utils.mapping.map(lat, lon, criteria, marker=None, color=None, projection='auto', proj_default=True, crit_dist=5000, background=True, borders=False, rivers=False, lakes=False, figsize=None, ax=None, scatter_kwargs=None, legend=True, legend_title=None, lgd_kwargs=None, savefig_settings=None)[source]
Map the location of all lat/lon according to some criteria
DEPRECATED: use scatter_map() instead
Map the location of all lat/lon according to some criteria. Based on functions defined in the Cartopy package.
- Parameters
lat (list) – a list of latitudes.
lon (list) – a list of longitudes.
criteria (list) – a list of unique criteria for plotting purposes. For instance, a map by the types of archive present in the dataset or proxy observations. Should have the same length as lon/lat.
marker (list) – a list of possible markers for each criterion. If None, will use pyleoclim default
color (list) – a list of possible colors for each criterion. If None, will use pyleoclim default
projection (string) – the map projection. Available projections: ‘Robinson’ (default), ‘PlateCarree’, ‘AlbertsEqualArea’, ‘AzimuthalEquidistant’,’EquidistantConic’,’LambertConformal’, ‘LambertCylindrical’,’Mercator’,’Miller’,’Mollweide’,’Orthographic’, ‘Sinusoidal’,’Stereographic’,’TransverseMercator’,’UTM’, ‘InterruptedGoodeHomolosine’,’RotatedPole’,’OSGB’,’EuroPP’, ‘Geostationary’,’NearsidePerspective’,’EckertI’,’EckertII’, ‘EckertIII’,’EckertIV’,’EckertV’,’EckertVI’,’EqualEarth’,’Gnomonic’, ‘LambertAzimuthalEqualArea’,’NorthPolarStereo’,’OSNI’,’SouthPolarStereo’ By default, projection == ‘auto’, so the projection will be picked based on the degree of clustering of the sites.
proj_default (bool) – If True, uses the standard projection attributes. Enter new attributes in a dictionary to change them. Lists of attributes can be found in the Cartopy documentation.
crit_dist (float) – critical radius for projection choice. Default: 5000 km Only active if projection == ‘auto’
background (bool) – If True, uses a shaded relief background (only one available in Cartopy)
borders (bool) – Draws the countries border. Defaults is off (False).
rivers (bool) – Draws major rivers. Default is off (False).
lakes (bool) – Draws major lakes. Default is off (False).
figsize (list) – the size for the figure
ax (axis,optional) – Return as axis instead of figure (useful to integrate plot into a subplot)
scatter_kwargs (dict) – Dictionary of arguments available in matplotlib.pyplot.scatter.
legend (bool) – Whether the draw a legend on the figure
legend_title (str) – Use this instead of a dynamic range for legend
lgd_kwargs (dict) – Dictionary of arguments for matplotlib.pyplot.legend.
savefig_settings (dict) –
Dictionary of arguments for matplotlib.pyplot.saveFig.
”path” must be specified; it can be any existed or non-existed path, with or without a suffix; if the suffix is not given in “path”, it will follow “format”
”format” can be one of {“pdf”, “eps”, “png”, “ps”}
- Returns
ax
- Return type
The figure, or axis if ax specified
See also
pyleoclim.utils.mapping.set_proj
Set the projection for Cartopy-based maps
pyleoclim.utils.mapping.pick_proj
pick the projection type based on the degree of clustering of coordinates
- pyleoclim.utils.mapping.pick_proj(lat, lon, crit_dist=5000)[source]
Pick projection based on the degree of clustering of coordinates. At the moment, returns only one of two options:
‘Robinson’ for R > crit_dist
‘Orthographic’ for R <= crit_dist
- Parameters
lat (1d array) – latitudes in [-90, 90]
lon (1d array) – longitudes in (-180, 180]
crit_dist (float) – critical radius. Default: 5000 km
- Returns
proj – ‘Orthographic’ or ‘Robinson’
- Return type
str
- pyleoclim.utils.mapping.scatter_map(geos, hue='archiveType', size=None, marker='archiveType', edgecolor='k', proj_default=True, projection='auto', crit_dist=5000, background=True, borders=False, coastline=True, rivers=False, lakes=False, ocean=True, land=True, figsize=None, scatter_kwargs=None, gridspec_kwargs=None, extent='global', lgd_kwargs=None, legend=True, colorbar=True, cmap=None, fig=None, gs_slot=None, **kwargs)[source]
- Parameters
geos (Pandas DataFrame, GeoSeries, MultipleGeoSeries, required) – If a Pandas DataFrame, expects ‘lat’ and ‘lon’ columns
hue (string, optional) – Grouping variable that will produce points with different colors. Can be either categorical or numeric, although color mapping will behave differently in latter case. The default is ‘archiveType’.
size (string, optional) – Grouping variable that will produce points with different sizes. Expects to be numeric. Any data without a value for the size variable will be filtered out. The default is None.
marker (string, optional) – Grouping variable that will produce points with different markers. Can have a numeric dtype but will always be treated as categorical. The default is ‘archiveType’.
edgecolor (color (string) or list of rgba tuples, optional) – Color of marker edge. The default is ‘w’.
projection (string) – the map projection. Available projections: ‘Robinson’ (default), ‘PlateCarree’, ‘AlbertsEqualArea’, ‘AzimuthalEquidistant’,’EquidistantConic’,’LambertConformal’, ‘LambertCylindrical’,’Mercator’,’Miller’,’Mollweide’,’Orthographic’, ‘Sinusoidal’,’Stereographic’,’TransverseMercator’,’UTM’, ‘InterruptedGoodeHomolosine’,’RotatedPole’,’OSGB’,’EuroPP’, ‘Geostationary’,’NearsidePerspective’,’EckertI’,’EckertII’, ‘EckertIII’,’EckertIV’,’EckertV’,’EckertVI’,’EqualEarth’,’Gnomonic’, ‘LambertAzimuthalEqualArea’,’NorthPolarStereo’,’OSNI’,’SouthPolarStereo’ By default, projection == ‘auto’, so the projection will be picked based on the degree of clustering of the sites.
proj_default (bool, optional) –
If True, uses the standard projection attributes. Enter new attributes in a dictionary to change them. Lists of attributes can be found in the Cartopy documentation. The default is True.
crit_dist (float, optional) – critical radius for projection choice. Default: 5000 km Only active if projection == ‘auto’
background (bool, optional) – If True, uses a shaded relief background (only one available in Cartopy)
borders (bool, optional) – Draws the countries border. Defaults is off (False).
rivers (bool, optional) – Draws major rivers. Default is off (False).
lakes (bool, optional) – Draws major lakes. Default is off (False).
figsize (list or tuple, optional) – Size for the figure
scatter_kwargs (dict, optional) –
Dict of arguments available in seaborn.scatterplot. Dictionary of arguments available in matplotlib.pyplot.scatter.
legend (bool, optional) – Whether the draw a legend on the figure. Default is True.
colorbar (bool, optional) – Whether the draw a colorbar on the figure if the data associated with hue are numeric. Default is True.
lgd_kwargs (dict, optional) –
Dictionary of arguments for matplotlib.pyplot.legend.
savefig_settings (dict, optional) –
Dictionary of arguments for matplotlib.pyplot.saveFig.
”path” must be specified; it can be any existed or non-existed path, with or without a suffix; if the suffix is not given in “path”, it will follow “format”
”format” can be one of {“pdf”, “eps”, “png”, “ps”}
extent (TYPE, optional) – DESCRIPTION. The default is ‘global’.
cmap (string or list, optional) – Matplotlib supported colormap id or list of colors for creating a colormap. See choosing a matplotlib colormap. The default is None.
fig (matplotlib.pyplot.figure, optional) – See matplotlib.pyplot.figure <https://matplotlib.org/3.5.0/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib-pyplot-figure>_. The default is None.
gs_slot (Gridspec slot, optional) – If generating a map for a multi-plot, pass a gridspec slot. The default is None.
gridspec_kwargs (dict, optional) – Function assumes the possibility of a colorbar, map, and legend. A list of floats associated with the keyword width_ratios will assume the first (index=0) is the relative width of the colorbar, the second to last (index = -2) is the relative width of the map, and the last (index = -1) is the relative width of the area for the legend. For information about Gridspec configuration, refer to `Matplotlib documentation <https://matplotlib.org/3.5.0/api/_as_gen/matplotlib.gridspec.GridSpec.html#matplotlib.gridspec.GridSpec>_. The default is None.
kwargs (dict, optional) –
‘missing_val_hue’, ‘missing_val_marker’, ‘missing_val_label’ can all be used to change the way missing values are represented (‘k’, ‘?’, are default hue and marker values will be associated with the label: ‘missing’).
’hue_mapping’ and ‘marker_mapping’ can be used to submit dictionaries mapping hue values to colors and marker values to markers. Does not replace passing a string value for hue or marker.
- Raises
TypeError – DESCRIPTION.
- Returns
fig, dictionary of ax objects which includes the as many as three items: ‘cb’ (colorbar ax), ‘map’ (scatter map), and ‘leg’ (legend ax)
- Return type
TYPE
See also
pyleoclim.utils.mapping.set_proj
Set the projection for Cartopy-based maps
pyleoclim.utils.mapping.pick_proj
pick the projection type based on the degree of clustering of coordinates
- pyleoclim.utils.mapping.set_proj(projection='Robinson', proj_default=True)[source]
Set the projection for Cartopy.
- Parameters
projection (string) – the map projection. Available projections: ‘Robinson’ (default), ‘PlateCarree’, ‘AlbertsEqualArea’, ‘AzimuthalEquidistant’,’EquidistantConic’,’LambertConformal’, ‘LambertCylindrical’,’Mercator’,’Miller’,’Mollweide’,’Orthographic’, ‘Sinusoidal’,’Stereographic’,’TransverseMercator’,’UTM’, ‘InterruptedGoodeHomolosine’,’RotatedPole’,’OSGB’,’EuroPP’, ‘Geostationary’,’NearsidePerspective’,’EckertI’,’EckertII’, ‘EckertIII’,’EckertIV’,’EckertV’,’EckertVI’,’EqualEarth’,’Gnomonic’, ‘LambertAzimuthalEqualArea’,’NorthPolarStereo’,’OSNI’,’SouthPolarStereo’
proj_default (bool; {True,False}) –
If True, uses the standard projection attributes from Cartopy. Enter new attributes in a dictionary to change them. Lists of attributes can be found in the Cartopy documentation.
- Returns
proj
- Return type
the Cartopy projection object
See also
pyleoclim.utils.mapping.map
mapping function making use of the projection
Plotting
Plotting utilities, leveraging Matplotlib.
- pyleoclim.utils.plotting.closefig(fig=None)[source]
Close the figure
- Parameters
fig (matplotlib.pyplot.figure) – The matplotlib figure object
- pyleoclim.utils.plotting.plot_scatter_xy(x1, y1, x2, y2, figsize=None, xlabel=None, ylabel=None, title=None, xlim=None, ylim=None, savefig_settings=None, ax=None, legend=True, plot_kwargs=None, lgd_kwargs=None)[source]
Plot a scatter on top of a line plot.
- Parameters
x1 (array) – x axis of timeseries1 - plotted as a line
y1 (array) – values of timeseries1 - plotted as a line
x2 (array) – x axis of scatter points
y2 (array) – y of scatter points
figsize (list) – a list of two integers indicating the figure size
xlabel (str) – label for x-axis
ylabel (str) – label for y-axis
title (str) – the title for the figure
xlim (list) – set the limits of the x axis
ylim (list) – set the limits of the y axis
ax (pyplot.axis) – the pyplot.axis object
legend (bool) – plot legend or not
lgd_kwargs (dict) – the keyword arguments for ax.legend()
plot_kwargs (dict) – the keyword arguments for ax.plot()
savefig_settings (dict) –
the dictionary of arguments for plt.savefig(); some notes below: - “path” must be specified; it can be any existing or non-existing path,
with or without a suffix; if the suffix is not given in “path”, it will follow “format”
”format” can be one of {“pdf”, “eps”, “png”, “ps”}
- Returns
ax
- Return type
the pyplot.axis object
See also
pyleoclim.utils.plotting.set_style
set different styles for the figures. Should be set before invoking the plotting functions
pyleoclim.utils.plotting.savefig
save figures
- pyleoclim.utils.plotting.plot_xy(x, y, figsize=None, xlabel=None, ylabel=None, title=None, xlim=None, ylim=None, savefig_settings=None, ax=None, legend=True, plot_kwargs=None, lgd_kwargs=None, invert_xaxis=False, invert_yaxis=False)[source]
Plot a timeseries
- Parameters
x (array) – The time axis for the timeseries
y (array) – The values of the timeseries
figsize (list) – a list of two integers indicating the figure size
xlabel (str) – label for x-axis
ylabel (str) – label for y-axis
title (str) – the title for the figure
xlim (list) – set the limits of the x axis
ylim (list) – set the limits of the y axis
ax (pyplot.axis) – the pyplot.axis object
legend (bool) – plot legend or not
lgd_kwargs (dict) – the keyword arguments for ax.legend()
plot_kwargs (dict) – the keyword arguments for ax.plot()
mute (bool) –
if True, the plot will not show; recommend to turn on when more modifications are going to be made on ax
(going to be deprecated)
savefig_settings (dict) –
the dictionary of arguments for plt.savefig(); some notes below: - “path” must be specified; it can be any existing or non-existing path,
with or without a suffix; if the suffix is not given in “path”, it will follow “format”
”format” can be one of {“pdf”, “eps”, “png”, “ps”}
invert_xaxis (bool, optional) – if True, the x-axis of the plot will be inverted
invert_yaxis (bool, optional) – if True, the y-axis of the plot will be inverted
- Returns
ax
- Return type
the pyplot.axis object
See also
pyleoclim.utils.plotting.set_style
set different styles for the figures. Should be set before invoking the plotting functions
pyleoclim.utils.plotting.savefig
save figures
- pyleoclim.utils.plotting.savefig(fig, path=None, dpi=300, settings={}, verbose=True)[source]
Save a figure to a path
- Parameters
fig (matplotlib.pyplot.figure) – the figure to save
path (str) – the path to save the figure, can be ignored and specify in “settings” instead
dpi (int) – resolution in dot (pixels) per inch. Default: 300.
settings (dict) –
the dictionary of arguments for plt.savefig(); some notes below: - “path” must be specified in settings if not assigned with the keyword argument;
it can be any existing or non-existing path, with or without a suffix; if the suffix is not given in “path”, it will follow “format”
”format” can be one of {“pdf”, “eps”, “png”, “ps”}
verbose (bool, {True,False}) – If True, print the path of the saved file.
- pyleoclim.utils.plotting.scatter_xy(x, y, c=None, figsize=None, xlabel=None, ylabel=None, title=None, xlim=None, ylim=None, savefig_settings=None, ax=None, legend=True, plot_kwargs=None, lgd_kwargs=None)[source]
Make scatter plot.
- Parameters
x (numpy.array) – x value
y (numpy.array) – y value
c (TYPE, optional) – DESCRIPTION. The default is None.
figsize (list, optional) – A list of two integers indicating the dimension of the figure. The default is None.
xlabel (str, optional) – x-axis label. The default is None.
ylabel (str, optional) – y-axis label. The default is None.
title (str, optional) – Title for the plot. The default is None.
xlim (list, optional) – Limits for the x-axis. The default is None.
ylim (list, optional) – Limits for the y-axis. The default is None.
savefig_settings (dict, optional) –
- the dictionary of arguments for plt.savefig(); some notes below:
”path” must be specified; it can be any existing or non-existing path, with or without a suffix; if the suffix is not given in “path”, it will follow “format”
”format” can be one of {“pdf”, “eps”, “png”, “ps”}
The default is None.
ax (pyplot.axis, optional) – The axis object. The default is None.
legend (bool, optional) – Whether to include a legend. The default is True.
plot_kwargs (dict, optional) – the keyword arguments for ax.plot(). The default is None.
lgd_kwargs (dict, optional) – the keyword arguments for ax.legend(). The default is None.
- Returns
ax
- Return type
the pyplot.axis object
- pyleoclim.utils.plotting.set_style(style='journal', font_scale=1.0, dpi=300)[source]
Modify the visualization style
This function is inspired by Seaborn.
- Parameters
style ({journal,web,matplotlib,_spines, _nospines,_grid,_nogrid}) –
set the styles for the figure:
journal (default): fonts appropriate for paper
web: web-like font (e.g. ggplot)
matplotlib: the original matplotlib style
In addition, the following options are available:
_spines/_nospines: allow to show/hide spines
_grid/_nogrid: allow to show gridlines (default: _grid)
font_scale (float) – Default is 1. Corresponding to 12 Font Size.
Spectral
Utilities for spectral analysis, including WWZ, CWT, Lomb-Scargle, MTM, and Welch. Designed for NumPy arrays, either evenly spaced or not (method-dependent).
All spectral methods must return a dictionary containing one vector for the frequency axis and the power spectral density (PSD).
Additional utilities help compute an optimal frequency vector or estimate scaling exponents.
- pyleoclim.utils.spectral.beta2Hurst(beta)[source]
Translates spectral slope to Hurst exponent
- Parameters
beta (float) – the estimated slope of a power spectral density :math: S(f) propto 1/f^{eta}
- Returns
H – Hurst index, should be in (0, 1)
- Return type
float
See also
pyleoclim.utils.spectral.beta_estimation
Estimate the scaling exponent of a power spectral density.
- pyleoclim.utils.spectral.beta_estimation(psd, freq, fmin=None, fmax=None, logf_binning_step='max', verbose=False)[source]
Estimate the scaling exponent of a power spectral density.
Models the spectrum as :math: S(f) propto 1/f^{eta}. For instance: - :math: eta = 0 corresponds to white noise - :math: eta = 1 corresponds to pink noise - :math: eta = 2 corresponds to red noise (Brownian motion)
- Parameters
psd (array) – the power spectral density
freq (array) – the frequency vector
fmin (float) – the min of frequency range for beta estimation
fmax (float) – the max of frequency range for beta estimation
verbose (bool) – if True, will print out debug information
- Returns
beta (float) – the estimated slope
f_binned (array) – binned frequency vector
psd_binned (array) – binned power spectral density
Y_reg (array) – prediction based on linear regression
- pyleoclim.utils.spectral.cwt_psd(ys, ts, freq=None, freq_method='log', freq_kwargs=None, scale=None, detrend=False, sg_kwargs={}, gaussianize=False, standardize=True, pad=False, mother='MORLET', param=None, cwt_res=None)[source]
Spectral estimation using the continuous wavelet transform Uses the Torrence and Compo [1998] continuous wavelet transform implementation
- Parameters
ys (numpy.array) – the time series.
ts (numpy.array) – the time axis.
freq (numpy.array, optional) – The frequency vector. The default is None, which will prompt the use of one the underlying functions
freq_method (string, optional) – The method by which to obtain the frequency vector. The default is ‘log’. Options are ‘log’ (default), ‘nfft’, ‘lomb_scargle’, ‘welch’, and ‘scale’
freq_kwargs (dict, optional) – Optional parameters for the choice of the frequency vector. See make_freq_vector and additional methods for details. The default is {}.
scale (numpy.array) – Optional scale vector in place of a frequency vector. Default is None. If scale is not None, frequency method and attached arguments will be ignored.
detrend (bool, string, {'linear', 'constant', 'savitzy-golay', 'emd'}) – Whether to detrend and with which option. The default is False.
sg_kwargs (dict, optional) – Additional parameters for the savitzy-golay method. The default is {}.
gaussianize (bool, optional) – Whether to gaussianize. The default is False.
standardize (bool, optional) – Whether to standardize. The default is True.
pad (bool, optional) – Whether or not to pad the timeseries. with zeroes to get N up to the next higher power of 2. This prevents wraparound from the end of the time series to the beginning, and also speeds up the FFT’s used to do the wavelet transform. This will not eliminate all edge effects. The default is False.
mother (string, optional) – the mother wavelet function. The default is ‘MORLET’. Options are: ‘MORLET’, ‘PAUL’, or ‘DOG’
param (flaot, option) –
the mother wavelet parameter. The default is None since it varies for each mother
For ‘MORLET’ this is k0 (wavenumber), default is 6.
For ‘PAUL’ this is m (order), default is 4.
For ‘DOG’ this is m (m-th derivative), default is 2.
cwt_res (dict) – Results from pyleoclim.utils.wavelet.cwt
- Returns
res –
- Dictionary containing:
psd: the power density function
freq: frequency vector
scale: the scale vector
mother: the mother wavelet
param : the wavelet parameter
- Return type
dict
See also
pyleoclim.utils.wavelet.make_freq_vector
make the frequency vector with various methods
pyleoclim.utils.wavelet.cwt
Torrence and Compo implementation of the continuous wavelet transform
pyleoclim.utils.spectral.periodogram
Spectral estimation using Blackman-Tukey’s periodogram
pyleoclim.utils.spectral.mtm
Spectral estimation using the multi-taper method
pyleoclim.utils.spectral.lomb_scargle
Spectral estimation using the lomb-scargle periodogram
pyleoclim.utils.spectral.welch
Spectral estimation using Welch’s periodogram
pyleoclim.utils.spectral.wwz_psd
Spectral estimation using the Weighted Wavelet Z-transform
pyleoclim.utils.tsutils.detrend
detrending functionalities using 4 possible methods
pyleoclim.utils.tsutils.gaussianize
Quantile maps a 1D array to a Gaussian distribution
pyleoclim.utils.tsutils.standardize
Centers and normalizes a given time series.
References
Torrence, C. and G. P. Compo, 1998: A Practical Guide to Wavelet Analysis. Bull. Amer. Meteor. Soc., 79, 61-78. Python routines available at http://paos.colorado.edu/research/wavelets/
- pyleoclim.utils.spectral.lomb_scargle(ys, ts, freq=None, freq_method='lomb_scargle', freq_kwargs=None, n50=3, window='hann', detrend=None, sg_kwargs=None, gaussianize=False, standardize=True, average='mean')[source]
Lomb-scargle priodogram
Appropriate for unevenly-spaced arrays. Uses the lomb-scargle implementation from scipy.signal: https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.lombscargle.html
- Parameters
ys (array) – a time series
ts (array) – time axis of the time series
freq (str or array) – vector of frequency. If string, uses the following method:
freq_method (str) –
Method to generate the frequency vector if not set directly. The following options are avialable:
log
lomb_scargle (default)
welch
scale
nfft
See utils.wavelet.make_freq_vector for details
freq_kwargs (dict) – Arguments for the method chosen in freq_method. See specific functions in utils.wavelet for details By default, uses dt=median(ts), ofac=4 and hifac=1 for Lomb-Scargle
n50 (int) – The number of 50% overlapping segment to apply
window (str or tuple) –
Desired window to use. Possible values:
boxcar
triang
blackman
hamming
hann (default)
bartlett
flattop
parzen
bohman
blackmanharris
nuttail
barthann
kaiser (needs beta)
gaussian (needs standard deviation)
general_gaussian (needs power, width)
slepian (needs width)
dpss (needs normalized half-bandwidth)
chebwin (needs attenuation)
exponential (needs decay scale)
tukey (needs taper fraction)
If the window requires no parameters, then window can be a string. If the window requires parameters, then window must be a tuple with the first argument the string name of the window, and the next arguments the needed parameters. If window is a floating point number, it is interpreted as the beta parameter of the kaiser window.
detrend : str
If None, no detrending is applied. Available detrending methods:
None - no detrending will be applied (default);
linear - a linear least-squares fit to ys is subtracted;
constant - the mean of ys is subtracted
savitzy-golay - ys is filtered using the Savitzky-Golay filters and the resulting filtered series is subtracted from y.
emd - Empirical mode decomposition
sg_kwargs : dict
The parameters for the Savitzky-Golay filters. see pyleoclim.utils.filter.savitzy_golay for details.
gaussianize : bool
If True, gaussianizes the timeseries
standardize : bool
If True, standardizes the timeseriesprep_args : dict
average : {‘mean’,’median’}
Method to use when averaging periodograms. Defaults to ‘mean’.
- Returns
res_dict – the result dictionary, including
freq (array): the frequency vector
psd (array): the spectral density vector
- Return type
dict
See also
pyleoclim.utils.spectral.periodogram
Estimate power spectral density using a periodogram
pyleoclim.utils.spectral.mtm
Retuns spectral density using a multi-taper method
pyleoclim.utils.spectral.welch
Returns power spectral density using the Welch method
pyleoclim.utils.spectral.wwz_psd
Spectral estimation using the Weighted Wavelet Z-transform
pyleoclim.utils.spectral.cwt_psd
Spectral estimation using the Continuous Wavelet Transform
pyleoclim.utils.filter.savitzy_golay
Filtering using Savitzy-Golay
pyleoclim.utils.tsutils.detrend
detrending functionalities using 4 possible methods
pyleoclim.utils.tsutils.gaussianize
Quantile maps a 1D array to a Gaussian distribution
pyleoclim.utils.tsutils.standardize
Centers and normalizes a given time series.
References
Lomb, N. R. (1976). Least-squares frequency analysis of unequally spaced data. Astrophysics and Space Science 39, 447-462.
Scargle, J. D. (1982). Studies in astronomical time series analysis. II. Statistical aspects of spectral analyis of unvenly spaced data. The Astrophysical Journal, 263(2), 835-853.
Scargle, J. D. (1982). Studies in astronomical time series analysis. II. Statistical aspects of spectral analyis of unvenly spaced data. The Astrophysical Journal, 263(2), 835-853.
- pyleoclim.utils.spectral.mtm(ys, ts, NW=None, BW=None, detrend=None, sg_kwargs=None, gaussianize=False, standardize=True, adaptive=False, jackknife=True, low_bias=True, sides='default', nfft=None)[source]
Spectral density using the multi-taper method.
If the NW product, or the BW and Fs in Hz are not specified by the user, a bandwidth of 4 times the fundamental frequency, corresponding to NW = 4 will be used.
Based on the nitime package: http://nipy.org/nitime/api/generated/nitime.algorithms.spectral.html
- Parameters
ys (array) – a time series
ts (array) – time axis of the time series
NW (float) – The time-bandwidth product NW governs the width (and therefore, height) of a peak, which can take the values [2, 5/2, 3, 7/2, 4]. This product controls the classical bias-variance tradeoff inherent to spectral estimation: a large product limits the variance but increases leakage out of harmonic line. In other words, small values of NW mean high spectral resolution, low bias, but high variance. Large values of the parameter mean lower resolution, higher bias, but reduced variance. There is no automated way to choose this parameter, and the default (NW=4) corresponds to a conservative choice with low variance. For a demonstration on the effect of this parameter, see the spectral analysis notebook in our tutorials: https://pyleoclim-util.readthedocs.io/en/master/tutorials.html.
BW (float) – The sampling-relative bandwidth of the data tapers
detrend (str) –
- If None, no detrending is applied. Available detrending methods:
None - no detrending will be applied (default);
linear - a linear least-squares fit to ys is subtracted;
constant - the mean of ys is subtracted
savitzy-golay - ys is filtered using the Savitzky-Golay filters and the resulting filtered series is subtracted from y.
emd - Empirical mode decomposition
- sg_kwargsdict
The parameters for the Savitzky-Golay filters. see pyleoclim.utils.filter.savitzy_golay for details.
- gaussianizebool
If True, gaussianizes the timeseries
- standardizebool
If True, standardizes the timeseries
- adaptive{True/False}
Use an adaptive weighting routine to combine the PSD estimates of different tapers.
- jackknife{True/False}
Use the jackknife method to make an estimate of the PSD variance at each point.
- low_bias{True/False}
Rather than use 2NW tapers, only use the tapers that have better than 90% spectral concentration within the bandwidth (still using a maximum of 2NW tapers)
- sidesstr (optional) [ ‘default’ | ‘onesided’ | ‘twosided’ ]
This determines which sides of the spectrum to return. For complex-valued inputs, the default is two-sided, for real-valued inputs, default is one-sided Indicates whether to return a one-sided or two-sided
- Returns
res_dict – the result dictionary, including - freq (array): the frequency vector - psd (array): the spectral density vector
- Return type
dict
See also
pyleoclim.utils.spectral.periodogram
Spectral density estimation using a Blackman-Tukey periodogram
pyleoclim.utils.spectral.welch
spectral estimation using Welch’s periodogram
pyleoclim.utils.spectral.lomb_scargle
Lomb-scargle priodogram
pyleoclim.utils.spectral.wwz_psd
Spectral estimation using the Weighted Wavelet Z-transform
pyleoclim.utils.spectral.cwt_psd
Spectral estimation using the Continuous Wavelet Transform
pyleoclim.utils.filter.savitzy_golay
Filtering using Savitzy-Golay
pyleoclim.utils.tsutils.detrend
detrending functionalities using 4 possible methods
pyleoclim.utils.tsutils.gaussianize
Quantile maps a 1D array to a Gaussian distribution
pyleoclim.utils.tsutils.standardize
Centers and normalizes a given time series.
- pyleoclim.utils.spectral.periodogram(ys, ts, window='hann', nfft=None, return_onesided=True, detrend=None, sg_kwargs=None, gaussianize=False, standardize=True, scaling='density')[source]
Spectral density estimation using a Blackman-Tukey periodogram
Based on the function from scipy.
- Parameters
ys (array) – a time series
ts (array) – time axis of the time series
window (string or tuple) –
Desired window to use. Possible values:
boxcar (default)
triang
blackman
hamming
hann
bartlett
flattop
parzen
bohman
blackmanharris
nuttail
barthann
kaiser (needs beta)
gaussian (needs standard deviation)
general_gaussian (needs power, width)
slepian (needs width)
dpss (needs normalized half-bandwidth)
chebwin (needs attenuation)
exponential (needs decay scale)
tukey (needs taper fraction)
If the window requires no parameters, then window can be a string. If the window requires parameters, then window must be a tuple with the first argument the string name of the window, and the next arguments the needed parameters. If window is a floating point number, it is interpreted as the beta parameter of the kaiser window.
nfft (int) – Length of the FFT used, if a zero padded FFT is desired. If None, the FFT length is nperseg
return_onesided (bool) – If True, return a one-sided spectrum for real data. If False return a two-sided spectrum. Defaults to True, but for complex data, a two-sided spectrum is always returned.
detrend (str) –
If None, no detrending is applied. Available detrending methods:
None - no detrending will be applied (default);
linear - a linear least-squares fit to ys is subtracted;
constant - the mean of ys is subtracted
savitzy-golay - ys is filtered using the Savitzky-Golay filters and the resulting filtered series is subtracted from y.
emd - Empirical mode decomposition
sg_kwargs (dict) – The parameters for the Savitzky-Golay filters. see pyleoclim.utils.filter.savitzy_golay for details.
gaussianize (bool) – If True, gaussianizes the timeseries
standardize (bool) – If True, standardizes the timeseries
scaling ({"density,"spectrum}) – Selects between computing the power spectral density (‘density’) where Pxx has units of V**2/Hz and computing the power spectrum (‘spectrum’) where Pxx has units of V**2, if x is measured in V and fs is measured in Hz. Defaults to ‘density’
- Returns
res_dict – the result dictionary, including
freq (array): the frequency vector
psd (array): the spectral density vector
- Return type
dict
See also
pyleoclim.utils.spectral.welch
Estimate power spectral density using the welch method
pyleoclim.utils.spectral.mtm
Retuns spectral density using a multi-taper method
pyleoclim.utils.spectral.lomb_scargle
Return the computed periodogram using lomb-scargle algorithm
pyleoclim.utils.spectral.wwz_psd
Spectral estimation using the Weighted Wavelet Z-transform
pyleoclim.utils.spectral.cwt_psd
Spectral estimation using the Continuous Wavelet Transform
pyleoclim.utils.filter.savitzy_golay
Filtering using Savitzy-Golay
pyleoclim.utils.tsutils.detrend
detrending functionalities using 4 possible methods
pyleoclim.utils.tsutils.gaussianize
Quantile maps a 1D array to a Gaussian distribution
pyleoclim.utils.tsutils.standardize
Centers and normalizes a given time series.
- pyleoclim.utils.spectral.psd_ar(var_noise, freq, ar_params, f_sampling)[source]
Theoretical power spectral density (PSD) of an autoregressive model
- Parameters
var_noise (float) – the variance of the noise of the AR process
freq (array) – vector of frequency
ar_params (array) – autoregressive coefficients, not including zero-lag
f_sampling (float) – sampling frequency
- Returns
psd – power spectral density
- Return type
array
- pyleoclim.utils.spectral.psd_fBM(freq, ts, H)[source]
Theoretical power spectral density of a fractional Brownian motion
- Parameters
freq (array) – vector of frequency
ts (array) – the time axis of the time series
H (float) – Hurst exponent, should be in (0, 1)
- Returns
psd – power spectral density
- Return type
array
References
Flandrin, P. On the spectrum of fractional Brownian motions. IEEE Transactions on Information Theory 35, 197–199 (1989).
- pyleoclim.utils.spectral.welch(ys, ts, window='hann', nperseg=None, noverlap=None, nfft=None, return_onesided=True, detrend=None, sg_kwargs=None, gaussianize=False, standardize=True, scaling='density', average='mean')[source]
Estimate power spectral density using Welch’s periodogram
Wrapper for the function implemented in scipy.signal.welch See https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.welch.html for details.
Welch’s method is an approach for spectral density estimation. It computes an estimate of the power spectral density by dividing the data into overlapping segments, computing a modified periodogram for each segment and averaging the periodograms to lower the estimator’s variance.
- Parameters
ys (array) – a time series
ts (array) – time axis of the time series
window (string or tuple) –
Desired window to use. Possible values:
boxcar
triang
blackman
hamming
hann (default)
bartlett
flattop
parzen
bohman
blackmanharris
nuttail
barthann
kaiser (needs beta)
gaussian (needs standard deviation)
general_gaussian (needs power, width)
slepian (needs width)
dpss (needs normalized half-bandwidth)
chebwin (needs attenuation)
exponential (needs decay scale)
tukey (needs taper fraction)
If the window requires no parameters, then window can be a string. If the window requires parameters, then window must be a tuple with the first argument the string name of the window, and the next arguments the needed parameters. If window is a floating point number, it is interpreted as the beta parameter of the kaiser window.
nperseg (int) – Length of each segment. If none, nperseg=len(ys)/2. Default to None This will give three segments with 50% overlap
noverlap (int) – Number of points to overlap. If None, noverlap=nperseg//2. Defaults to None, represents 50% overlap
nfft (int) – Length of the FFT used, if a zero padded FFT is desired. If None, the FFT length is nperseg
return_onesided (bool) – If True, return a one-sided spectrum for real data. If False return a two-sided spectrum. Defaults to True, but for complex data, a two-sided spectrum is always returned.
detrend (str) –
If None, no detrending is applied. Available detrending methods:
None - no detrending will be applied (default);
linear - a linear least-squares fit to ys is subtracted;
constant - the mean of ys is subtracted
savitzy-golay - ys is filtered using the Savitzky-Golay filters and the resulting filtered series is subtracted from y.
emd - Empirical mode decomposition
sg_kwargs (dict) – The parameters for the Savitzky-Golay filters. see pyleoclim.utils.filter.savitzy_golay for details.
gaussianize (bool) – If True, gaussianizes the timeseries
standardize (bool) – If True, standardizes the timeseries
scaling ({"density,"spectrum}) – Selects between computing the power spectral density (‘density’) where Pxx has units of V**2/Hz and computing the power spectrum (‘spectrum’) where Pxx has units of V**2, if x is measured in V and fs is measured in Hz. Defaults to ‘density’
average ({'mean','median'}) – Method to use when combining periodograms. Defaults to ‘mean’.
- Returns
res_dict – the result dictionary, including
freq (array): the frequency vector
psd (array): the spectral density vector
- Return type
dict
See also
pyleoclim.utils.spectral.periodogram
Spectral density estimation using a Blackman-Tukey periodogram
pyleoclim.utils.spectral.mtm
Spectral density estimation using the multi-taper method
pyleoclim.utils.spectral.lomb_scargle
Lomb-scargle priodogram
pyleoclim.utils.spectral.wwz_psd
Spectral estimation using the Weighted Wavelet Z-transform
pyleoclim.utils.spectral.cwt_psd
Spectral estimation using the Continuous Wavelet Transform
pyleoclim.utils.filter.savitzy_golay
Filtering using Savitzy-Golay
pyleoclim.utils.tsutils.detrend
detrending functionalities using 4 possible methods
pyleoclim.utils.tsutils.gaussianize
Quantile maps a 1D array to a Gaussian distribution
pyleoclim.utils.tsutils.standardize
Centers and normalizes a given time series.
References
- Welch, “The use of the fast Fourier transform for the estimation of power spectra:
A method based on time averaging over short, modified periodograms”, IEEE Trans. Audio Electroacoust. vol. 15, pp. 70-73, 1967.
- pyleoclim.utils.spectral.wwz_psd(ys, ts, freq=None, freq_method='log', freq_kwargs=None, tau=None, c=0.001, nproc=8, detrend=False, sg_kwargs=None, gaussianize=False, standardize=True, Neff_threshold=3, anti_alias=False, avgs=2, method='Kirchner_numba', wwa=None, wwz_Neffs=None, wwz_freq=None)[source]
Spectral estimation using the Weighted Wavelet Z-transform
The Weighted wavelet Z-transform (WWZ) is based on Morlet wavelet spectral estimation, using least squares minimization to suppress the energy leakage caused by data gaps. WWZ does not rely on interpolation or detrending, and is appropriate for unevenly-spaced datasets. In particular, we use the variant of Kirchner & Neal (2013), in which basis rotations mitigate the numerical instability that occurs in pathological cases with the original algorithm (Foster, 1996). The WWZ method has one adjustable parameter, a decay constant c that balances the time and frequency resolutions of the analysis. The smaller this constant is, the sharper the peaks. The default value is 1e-3 to obtain smooth spectra that lend themselves to better scaling exponent estimation, while still capturing the main periodicities.
Note that scalogram applications use the larger value (8π2)−1, justified elsewhere (Foster, 1996).
- Parameters
ys (array) – a time series, NaNs will be deleted automatically
ts (array) – the time points, if ys contains any NaNs, some of the time points will be deleted accordingly
freq (array) – vector of frequency
freq_method (str, {'log', 'lomb_scargle', 'welch', 'scale', 'nfft'}) –
Method to generate the frequency vector if not set directly. The following options are avialable:
’log’ (default)
’lomb_scargle’
’welch’
’scale’
’nfft’
See
pyleoclim.utils.wavelet.make_freq_vector()
for detailsfreq_kwargs (dict) – Arguments for the method chosen in freq_method. See specific functions in pyleoclim.utils.wavelet for details
tau (array) – the evenly-spaced time vector for the analysis, namely the time shift for wavelet analysis
c (float) – the decay constant that will determine the analytical resolution of frequency for analysis, the smaller the higher resolution; the default value 1e-3 is good for most of the spectral analysis cases
nproc (int) – the number of processes for multiprocessing
detrend (str, {None, 'linear', 'constant', 'savitzy-golay'}) –
Methods for detrending include:
None: the original time series is assumed to have no trend;
’linear’: a linear least-squares fit to ys is subtracted;
’constant’: the mean of ys is subtracted
’savitzy-golay’: ys is filtered using the Savitzky-Golay filters and the resulting filtered series is subtracted from y.
sg_kwargs (dict) – The parameters for the Savitzky-Golay filters. See
pyleoclim.utils.filter.savitzky_golay()
for details.gaussianize (bool) – If True, gaussianizes the timeseries
standardize (bool) – If True, standardizes the timeseries
method (string, {'Foster', 'Kirchner', 'Kirchner_f2py', 'Kirchner_numba'}) –
Available specific implementation of WWZ include:
’Foster’: the original WWZ method;
’Kirchner’: the method Kirchner adapted from Foster;
’Kirchner_f2py’: the method Kirchner adapted from Foster, implemented with f2py for acceleration;
’Kirchner_numba’: the method Kirchner adapted from Foster, implemented with Numba for acceleration (default);
Neff_threshold (int) – threshold for the effective number of points
anti_alias (bool) – If True, uses anti-aliasing
avgs (int) – flag for whether spectrum is derived from instantaneous point measurements (avgs<>1) OR from measurements averaged over each sampling interval (avgs==1)
wwa (array) – the weighted wavelet amplitude, returned from pyleoclim.utils.wavelet.wwz
wwz_Neffs (array) – the matrix of effective number of points in the time-scale coordinates, returned from pyleoclim.utils.wavelet.wwz
wwz_freq (array) – the returned frequency vector from pyleoclim.utils.wavelet.wwz
- Returns
res (namedtuple) – a namedtuple that includes below items
psd (array) – power spectral density
freq (array) – vector of frequency
See also
pyleoclim.utils.spectral.periodogram
Estimate power spectral density using a periodogram
pyleoclim.utils.spectral.mtm
Retuns spectral density using a multi-taper method
pyleoclim.utils.spectral.lomb_scargle
Return the computed periodogram using lomb-scargle algorithm
pyleoclim.utils.spectral.welch
Estimate power spectral density using the Welch method
pyleoclim.utils.spectral.cwt_psd
Spectral estimation using the Continuous Wavelet Transform
pyleoclim.utils.filter.savitzy_golay
Filtering using Savitzy-Golay
pyleoclim.utils.tsutils.detrend
detrending functionalities using 4 possible methods
pyleoclim.utils.tsutils.gaussianize
Quantile maps a 1D array to a Gaussian distribution
pyleoclim.utils.tsutils.standardize
Centers and normalizes a given time series.
References
Foster, G. (1996). Wavelets for period analysis of unevenly sampled time series. The Astronomical Journal, 112(4), 1709-1729.
Kirchner, J. W. (2005). Aliasin in 1/f^a noise spectra: origins, consequences, and remedies. Physical Review E covering statistical, nonlinear, biological, and soft matter physics, 71, 66110.
Kirchner, J. W. and Neal, C. (2013). Universal fractal scaling in stream chemistry and its impli-cations for solute transport and water quality trend detection. Proc Natl Acad Sci USA 110:12213–12218.
Tsmodel
Module for timeseries modeling
- pyleoclim.utils.tsmodel.ar1_fit(y, t=None)[source]
Return lag-1 autocorrelation
Returns the lag-1 autocorrelation from AR(1) fit OR persistence from tauest.
- Parameters
y (array) – The time series
t (array) – The time axis of that series
- Returns
g – Lag-1 autocorrelation coefficient (for evenly-spaced time series) OR estimated persistence (for unevenly-spaced time series)
- Return type
float
See also
pyleoclim.utils.tsbase.is_evenly_spaced
Check if a time axis is evenly spaced, within a given tolerance
pyleoclim.utils.tsmodel.tau_estimation
Estimates the temporal decay scale of an (un)evenly spaced time series.
- pyleoclim.utils.tsmodel.ar1_fit_evenly(y)[source]
Returns the lag-1 autocorrelation from AR(1) fit.
Uses statsmodels.tsa.arima.model.ARIMA. to calculate lag-1 autocorrelation
- Parameters
y (array) – Vector of (float) numbers as a time series
- Returns
g – Lag-1 autocorrelation coefficient
- Return type
float
- pyleoclim.utils.tsmodel.ar1_model(t, tau, output_sigma=1)[source]
Simulate AR(1) process with REDFIT
Simulate a (possibly irregularly-sampled) AR(1) process with given decay constant tau, à la REDFIT.
- Parameters
t (array) – Time axis of the time series
tau (float) – The averaged persistence
- Returns
y – The AR(1) time series
- Return type
array
References
- Schulz, M. & Mudelsee, M. REDFIT: estimating red-noise spectra directly from unevenly spaced
paleoclimatic time series. Computers & Geosciences 28, 421–426 (2002).
- pyleoclim.utils.tsmodel.ar1_sim(y, p, t=None)[source]
Simulate AR(1) process(es) with sample autocorrelation value
Produce p realizations of an AR(1) process of length n with lag-1 autocorrelation g calculated from y and (if provided) t
- Parameters
y (array) – a time series; NaNs not allowed
p (int) – column dimension (number of surrogates)
t (array) – the time axis of the series
- Returns
ysim – n by p matrix of simulated AR(1) vector
- Return type
array
See also
pyleoclim.utils.tsmodel.ar1_model
Simulates a (possibly irregularly-sampled) AR(1) process with given decay constant tau, à la REDFIT.
pyleoclim.utils.tsmodel.ar1_fit
Returns the lag-1 autocorrelation from AR(1) fit OR persistence from tauest.
pyleoclim.utils.tsmodel.ar1_fit_evenly
Returns the lag-1 autocorrelation from AR(1) fit assuming even temporal spacing.
pyleoclim.utils.tsmodel.tau_estimation
Estimates the temporal decay scale of an (un)evenly spaced time series.
- pyleoclim.utils.tsmodel.colored_noise(alpha, t, f0=None, m=None, seed=None)[source]
Generate a colored noise timeseries
- Parameters
alpha (float) – exponent of the 1/f^alpha noise
t (float) – time vector of the generated noise
f0 (float) – fundamental frequency
m (int) – maximum number of the waves, which determines the highest frequency of the components in the synthetic noise
- Returns
y – the generated 1/f^alpha noise
- Return type
array
See also
pyleoclim.utils.tsmodel.gen_ts
Generate pyleoclim.Series with timeseries models
References
Eq. (15) in Kirchner, J. W. Aliasing in 1/f(alpha) noise spectra: origins, consequences, and remedies. Phys Rev E Stat Nonlin Soft Matter Phys 71, 066110 (2005).
- pyleoclim.utils.tsmodel.colored_noise_2regimes(alpha1, alpha2, f_break, t, f0=None, m=None, seed=None)[source]
Generate a colored noise timeseries with two regimes
- Parameters
alpha1 (float) – the exponent of the 1/f^alpha noise
alpha2 (float) – the exponent of the 1/f^alpha noise
f_break (float) – the frequency where the scaling breaks
t (float) – time vector of the generated noise
f0 (float) – fundamental frequency
m (int) – maximum number of the waves, which determines the highest frequency of the components in the synthetic noise
- Returns
y – the generated 1/f^alpha noise
- Return type
array
See also
pyleoclim.utils.tsmodel.gen_ts
Generate pyleoclim.Series with timeseries models
References
Eq. (15) in Kirchner, J. W. Aliasing in 1/f(alpha) noise spectra: origins, consequences, and remedies. Phys Rev E Stat Nonlin Soft Matter Phys 71, 066110 (2005).
- pyleoclim.utils.tsmodel.gen_ar1_evenly(t, g, scale=1, burnin=50)[source]
Generate AR(1) series samples
Wrapper for the function statsmodels.tsa.arima_process.arma_generate_sample. used to generate an ARMA
- Parameters
t (array) – the time axis
g (float) – lag-1 autocorrelation
scale (float) – The standard deviation of noise.
burnin (int) – Number of observation at the beginning of the sample to drop. Used to reduce dependence on initial values.
- Returns
y – the generated AR(1) series
- Return type
array
See also
pyleoclim.utils.tsmodel.gen_ts
Generate pyleoclim.Series with timeseries models
- pyleoclim.utils.tsmodel.gen_ts(model, t=None, nt=1000, **kwargs)[source]
Generate pyleoclim.Series with timeseries models
- Parameters
model (str, {'colored_noise', 'colored_noise_2regimes', 'ar1'}) –
the timeseries model to use
colored_noise : colored noise with one scaling slope
colored_noise_2regimes : colored noise with two regimes of two different scaling slopes
ar1 : AR(1) series
t (array) – the time axis
nt (number of time points) – only works if ‘t’ is None, and it will use an evenly-spaced vector with nt points
kwargs (dict) – the keyward arguments for the specified timeseries model
- Returns
t, v – time axis and values
- Return type
NumPy arrays
See also
pyleoclim.utils.tsmodel.colored_noise
Generate a colored noise timeseries
pyleoclim.utils.tsmodel.colored_noise_2regimes
Generate a colored noise timeseries with two regimes
pyleoclim.utils.tsmodel.gen_ar1_evenly
Generate an AR(1) series
- pyleoclim.utils.tsmodel.tau_estimation(y, t)[source]
Estimates the temporal decay scale of an (un)evenly spaced time series.
Esimtates the temporal decay scale of an (un)evenly spaced time series. Uses scipy.optimize.minimize_scalar.
- Parameters
y (array) – A time series
t (array) – Time axis of the time series
- Returns
tau_est – The estimated persistence
- Return type
float
References
- Mudelsee, M. TAUEST: A Computer Program for Estimating Persistence in Unevenly Spaced Weather/Climate Time Series.
Comput. Geosci. 28, 69–72 (2002).
Wavelet
Utilities for wavelet analysis, including Weighted Wavelet Z-transform (WWZ) and Continuous Wavelet Transform (CWT) à la Torrence & Compo 1998.
Includes multiple options for WWZ (Fortran via f2py, numba, multiprocessing) and enables cross-wavelet transform with either WWZ or CWT.
Designed for NumPy arrays, either evenly spaced or not (method-dependent)
- class pyleoclim.utils.wavelet.AliasFilter[source]
Performing anti-alias filter on a psd
experimental: Use at your own risk
@author: fzhu
Methods
alias_filter
(freq, pwr, fs, fc, f_limit, avgs)The anti-aliasing filter
alias
misfit
model
- alias_filter(freq, pwr, fs, fc, f_limit, avgs)[source]
The anti-aliasing filter
- Parameters
freq (array) – vector of frequencies in power spectrum
pwr (array) – vector of spectral power corresponding to frequencies “freq”
fs (float) – sampling frequency
fc (float) – corner frequency for 1/f^2 steepening of power spectrum
f_limit (float) – lower frequency limit for estimating misfit of model-plus-alias spectrum vs. measured power
avgs (int) – flag for whether spectrum is derived from instantaneous point measurements (avgs<>1) OR from measurements averaged over each sampling interval (avgs==1)
- Returns
alpha (float) – best-fit exponent of power-law model
filtered_pwr (array) – vector of alias-filtered spectral power
model_pwr (array) – vector of modeled spectral power
aliased_pwr (array) – vector of modeled spectral power, plus aliases
References
Kirchner, J. W. Aliasing in 1/f(alpha) noise spectra: origins, consequences, and remedies. Phys Rev E Stat Nonlin Soft Matter Phys 71, 66110 (2005).
- pyleoclim.utils.wavelet.angle_sig(theta, nMC=1000, level=0.05)[source]
Calculates the mean angle and assesses the significance of its statistics.
In general, a consistent phase relationship will have low circular standard deviation (sigma <= sigma_lo) and high concentration (kappa >= kappa_hi).
- Parameters
theta (numpy.array) – array of phase angles
nMC (int) – number of Monte Carlo simulations to assess angle confidence interval if None, the simulation is not performed.
level (float) – significance level against which to gauge sigma and kappa. default: 0.05
- Returns
angle_mean (float) – mean angle
sigma (float) – circular standard deviation
kappa (float) – an estimate of the Von Mises distribution’s kappa parameter. kappa is a measure of concentration (a reciprocal measure of dispersion, so 1/kappa is analogous to the variance).
sigma_lo (float) – alpha-level quantile for sigma
kappa_hi (float) – (1-alpha)-level quantile for kappa
References
_[1] Grinsted, A., J. C. Moore, and S. Jevrejeva (2004), Application of the cross wavelet transform and wavelet coherence to geophysical time series, Nonlinear Processes in Geophysics, 11, 561–566.
_[2] Huber, R., Dutra, L. V., & da Costa Freitas, C. (2001, July). SAR interferogram phase filtering based on the Von Mises distribution. In IGARSS 2001. Scanning the Present and Resolving the Future. Proceedings. IEEE 2001 International Geoscience and Remote Sensing Symposium (Cat. No. 01CH37217) (Vol. 6, pp. 2816-2818). IEEE.
See also
pyleoclim.utils.wavelet.angle_stats
phase angle statistics
- pyleoclim.utils.wavelet.angle_stats(theta)[source]
Statistics of a phase angle
- Parameters
theta (numpy.array) – array of phase angles
- Returns
mean_theta (float) – mean angle
sigma (float) – circular standard deviation
kappa (float) – an estimate of the Von Mises distribution’s kappa parameter
References
_[1] Huber, R., Dutra, L. V., & da Costa Freitas, C. (2001, July). SAR interferogram phase filtering based on the Von Mises distribution. In IGARSS 2001. Scanning the Present and Resolving the Future. Proceedings. IEEE 2001 International Geoscience and Remote Sensing Symposium (Cat. No. 01CH37217) (Vol. 6, pp. 2816-2818). IEEE.
See also
pyleoclim.utils.wavelet.angle_sig
significance of phase angle statistics
- pyleoclim.utils.wavelet.assertPositiveInt(*args)[source]
Assert that the arguments are all integers larger than unity
- Parameters
args –
- pyleoclim.utils.wavelet.chisquare_inv(P, V)[source]
Returns the inverse of chi-square CDF with V degrees of freedom at fraction P
- Parameters
P (float) – fraction
V (float) – degress of freedom
- Returns
X – Inverse chi-square
- Return type
float
References
Torrence, C. and G. P. Compo, 1998: A Practical Guide to Wavelet Analysis. Bull. Amer. Meteor. Soc., 79, 61-78. Python routines available at http://paos.colorado.edu/research/wavelets/
- pyleoclim.utils.wavelet.chisquare_solve(XGUESS, P, V)[source]
Given XGUESS, a percentile P, and degrees-of-freedom V, return the difference between calculated percentile and P.
- Parameters
XGUESS (float) – sig level
P (float) – percentile
V (float) – degrees of freedom
- Returns
PDIFF – difference between calculated percentile and P
- Return type
float
References
Torrence, C. and G. P. Compo, 1998: A Practical Guide to Wavelet Analysis. Bull. Amer. Meteor. Soc., 79, 61-78. Python routines available at http://paos.colorado.edu/research/wavelets/
- pyleoclim.utils.wavelet.cwt(ys, ts, freq=None, freq_method='log', freq_kwargs={}, scale=None, detrend=False, sg_kwargs={}, gaussianize=False, standardize=True, pad=False, mother='MORLET', param=None)[source]
Wrapper function to implement Torrence and Compo continuous wavelet transform
- Parameters
ys (numpy.array) – the time series.
ts (numpy.array) – the time axis.
freq (numpy.array, optional) – The frequency vector. The default is None, which will prompt the use of one the underlying functions
freq_method (string, optional) – The method by which to obtain the frequency vector. The default is ‘log’. Options are ‘log’ (default), ‘nfft’, ‘lomb_scargle’, ‘welch’, and ‘scale’
freq_kwargs (dict, optional) – Optional parameters for the choice of the frequency vector. See make_freq_vector and additional methods for details. The default is {}.
scale (numpy.array) – Optional scale vector in place of a frequency vector. Default is None. If scale is not None, frequency method and attached arguments will be ignored.
detrend (bool, string, {'linear', 'constant', 'savitzy-golay', 'emd'}) – Whether to detrend and with which option. The default is False.
sg_kwargs (dict, optional) – Additional parameters for the savitzy-golay method. The default is {}.
gaussianize (bool, optional) – Whether to gaussianize. The default is False.
standardize (bool, optional) – Whether to standardize. The default is True.
pad (bool, optional) – Whether or not to pad the timeseries. with zeroes to get N up to the next higher power of 2. This prevents wraparound from the end of the time series to the beginning, and also speeds up the FFT’s used to do the wavelet transform. This will not eliminate all edge effects. The default is False.
mother (string, optional) – the mother wavelet function. The default is ‘MORLET’. Options are: ‘MORLET’, ‘PAUL’, or ‘DOG’
param (flaot, optional) –
- the mother wavelet parameter. The default is None since it varies for each mother
For ‘MORLET’ this is k0 (wavenumber), default is 6.
For ‘PAUL’ this is m (order), default is 4.
For ‘DOG’ this is m (m-th derivative), default is 2.
- Returns
res –
- Dictionary containing:
amplitude: the wavelet amplitude
coi: cone of influence
freq: frequency vector
coeff: the wavelet coefficients
scale: the scale vector
time: the time vector
mother: the mother wavelet
param : the wavelet parameter
- Return type
dict
See also
pyleoclim.utils.wavelet.make_freq_vector
make the frequency vector with various methods
pyleoclim.utils.wavelet.tc_wavelet
the underlying wavelet function by Torrence and Compo
pyleoclim.utils.tsutils.detrend
detrending functionalities
pyleoclim.utils.tsutils.gaussianize
Quantile maps a 1D array to a Gaussian distribution
pyleoclim.utils.tsutils.preprocess
pre-processes a times series using Gaussianization and detrending.
References
Torrence, C. and G. P. Compo, 1998: A Practical Guide to Wavelet Analysis. Bull. Amer. Meteor. Soc., 79, 61-78. Python routines available at http://paos.colorado.edu/research/wavelets/
- pyleoclim.utils.wavelet.cwt_coherence(ys1, ts1, ys2, ts2, freq=None, freq_method='log', freq_kwargs={}, scale=None, detrend=False, sg_kwargs={}, pad=False, standardize=True, gaussianize=False, tau=None, Neff_threshold=3, mother='MORLET', param=None, smooth_factor=0.25)[source]
Returns the wavelet transform coherency of two time series using the CWT.
- Parameters
ys1 (array) – first of two time series
ys2 (array) – second of the two time series
ts1 (array) – time axis of first time series
ts2 (array) – time axis of the second time series (should be = ts1)
tau (array) – evenly-spaced time points at which to evaluate coherence Defaults to None, which uses ts1
freq (array) – vector of frequency
freq_method (string, optional) – The method by which to obtain the frequency vector. The default is ‘log’. Options are ‘log’ (default), ‘nfft’, ‘lomb_scargle’, ‘welch’, and ‘scale’
freq_kwargs (dict, optional) – Optional parameters for the choice of the frequency vector. See make_freq_vector and additional methods for details. The default is {}.
scale (numpy.array) – Optional scale vector in place of a frequency vector. Default is None. If scale is not None, frequency method and attached arguments will be ignored.
detrend (bool, string, {'linear', 'constant', 'savitzy-golay', 'emd'}) – Whether to detrend and with which option. The default is False.
sg_kwargs (dict, optional) – Additional parameters for the savitzy-golay method. The default is {}.
gaussianize (bool, optional) – Whether to gaussianize. The default is False.
standardize (bool, optional) – Whether to standardize. The default is True.
pad (bool, optional) – Whether or not to pad the timeseries with zeroes to increase N to the next higher power of 2. This prevents wraparound from the end of the time series to the beginning, and also speeds up the FFT used to do the wavelet transform. This will not eliminate all edge effects. The default is False.
mother (string, optional) – the mother wavelet function. The default is ‘MORLET’. Options are: ‘MORLET’, ‘PAUL’, or ‘DOG’
param (float, optional) –
- the mother wavelet parameter. The default is None since it varies for each mother
For ‘MORLET’ this is k0 (wavenumber), default is 6.
For ‘PAUL’ this is m (order), default is 4.
For ‘DOG’ this is m (m-th derivative), default is 2.
smooth_factor (float) – smoothing factor for the WTC (default: 0.25)
Neff_threshold (int) – threshold for the effective number of points (3 by default, see make_coi())
- Returns
res – contains the cross wavelet coherence (WTC), cross-wavelet transform (XWT), cross-wavelet phase, vector of frequency, evenly-spaced time points, nMC AR1 scalograms, cone of influence.
- Return type
dict
References
Grinsted, A., J. C. Moore, and S. Jevrejeva (2004), Application of the cross wavelet transform and wavelet coherence to geophysical time series, Nonlinear Processes in Geophysics, 11, 561–566.
See also
pyleoclim.utils.wavelet.cwt
Continuous Wavelet Transform (Torrence & Compo 1998)
pyleoclim.utils.filter.savitzky_golay
Smooth (and optionally differentiate) data with a Savitzky-Golay filter.
pyleoclim.utils.wavelet.make_freq_vector
Makes frequency vector
pyleoclim.utils.tsutils.gaussianize
Quantile maps a 1D array to a Gaussian distribution
pyleoclim.utils.tsutils.detrend
detrending functionalities
pyleoclim.utils.tsutils.preprocess
pre-processes a times series using Gaussianization and detrending.
- pyleoclim.utils.wavelet.freq_vector_log(ts, nfreq=None)[source]
Return the frequency vector based on logspace
- Parameters
ts (array) – time axis of the time series
nv (int) – the parameter that controls the number of freq points
- Returns
freq – the frequency vector
- Return type
array
See also
pyleoclim.utils.wavelet.freq_vector_lomb_scargle
Return the frequency vector based on the REDFIT recommendation.
pyleoclim.utils.wavelet.freq_vector_welch
Return the frequency vector based on the Welch’s method.
pyleoclim.utils.wavelet.freq_vector_nfft
Return the frequency vector based on NFFT
pyleoclim.utils.wavelet.freq_vector_scale
Return the frequency vector based on scales
pyleoclim.utils.wavelet.make_freq_vector
Make frequency vector
- pyleoclim.utils.wavelet.freq_vector_lomb_scargle(ts, dt=None, nf=None, ofac=4, hifac=1)[source]
Return the frequency vector based on the REDFIT recommendation.
- Parameters
ts (array) – time axis of the time series
dt (float) – The resolution of the data. If None, uses the median resolution. Defaults to None.
nf (int) – Number of frequency points. If None, calculated as the difference between the highest and lowest frequencies (set by hifac and ofac) divided by resolution. Defaults to None
ofac (float) –
- Oversampling rate that influences the resolution of the frequency axis,
when equals to 1, it means no oversamling (should be >= 1). The default value 4 is usually a good value.
hifac (float) – fhi/fnyq (should be <= 1), where fhi is the highest frequency that can be analyzed by the Lomb-Scargle algorithm and fnyq is the Nyquist frequency.
- Returns
freq – the frequency vector
- Return type
array
References
Trauth, M. H. MATLAB® Recipes for Earth Sciences. (Springer, 2015). pp 181.
See also
pyleoclim.utils.wavelet.freq_vector_welch
Return the frequency vector based on the Welch’s method.
pyleoclim.utils.wavelet.freq_vector_nfft
Return the frequency vector based on NFFT
pyleoclim.utils.wavelet.freq_vector_scale
Return the frequency vector based on scales
pyleoclim.utils.wavelet.freq_vector_log
Return the frequency vector based on logspace
pyleoclim.utils.wavelet.make_freq_vector
Make frequency vector
- pyleoclim.utils.wavelet.freq_vector_nfft(ts)[source]
Return the frequency vector based on NFFT
- Parameters
ts (array) – time axis of the time series
- Returns
freq – the frequency vector
- Return type
array
See also
pyleoclim.utils.wavelet.freq_vector_lomb_scargle
Return the frequency vector based on the REDFIT recommendation.
pyleoclim.utils.wavelet.freq_vector_welch
Return the frequency vector based on the Welch’s method.
pyleoclim.utils.wavelet.freq_vector_scale
Return the frequency vector based on scales
pyleoclim.utils.wavelet.freq_vector_log
Return the frequency vector based on logspace
pyleoclim.utils.wavelet.make_freq_vector
Make frequency vector
- pyleoclim.utils.wavelet.freq_vector_scale(ts, dj=0.25, s0=None, j1=None, mother='MORLET', param=None)[source]
Return the frequency vector based on scales for wavelet analysis. This function is adapted from Torrence and Compo
- Parameters
ts (numpy.array) – The time axis for the timeseries
dj (float, optional) – The spacing between discrete scales. The default is 0.25. A smaller number will give better scale resolution, but be slower to plot.
s0 (float, optional) – the smallest scale of the wavelet. The default is None, representing 2*dT.
j1 (float, optional) – the number of scales minus one. Scales range from S0 up to S0*2**(J1*DJ), to give a total of (J1+1) scales. The default is None, which represents (LOG2(N DT/S0))/DJ.
mother (string, optional) – the mother wavelet function. The default is ‘MORLET’. Options are: ‘MORLET’, ‘PAUL’, or ‘DOG’
param (flaot, optional) –
the mother wavelet parameter. The default is None since it varies for each mother
For ‘MORLET’ this is k0 (wavenumber), default is 6.
For ‘PAUL’ this is m (order), default is 4.
For ‘DOG’ this is m (m-th derivative), default is 2.
- Returns
freq – the frequency vector
- Return type
array
See also
pyleoclim.utils.wavelet.freq_vector_lomb_scargle
Return the frequency vector based on the REDFIT recommendation.
pyleoclim.utils.wavelet.freq_vector_welch
Return the frequency vector based on the Welch’s method.
pyleoclim.utils.wavelet.freq_vector_nfft
Return the frequency vector based on NFFT
pyleoclim.utils.wavelet.freq_vector_log
Return the frequency vector based on logspace
pyleoclim.utils.wavelet.make_freq_vector
Make frequency vector
References
Torrence, C. and G. P. Compo, 1998: A Practical Guide to Wavelet Analysis. Bull. Amer. Meteor. Soc., 79, 61-78. Python routines available at http://paos.colorado.edu/research/wavelets/
- pyleoclim.utils.wavelet.freq_vector_welch(ts)[source]
Return the frequency vector based on Welch’s method.
- Parameters
ts (array) – time axis of the time series
- Returns
freq – the frequency vector
- Return type
array
References
https://github.com/scipy/scipy/blob/v0.14.0/scipy/signal/Spectral.py
See also
pyleoclim.utils.wavelet.freq_vector_lomb_scargle
Return the frequency vector based on the REDFIT recommendation.
pyleoclim.utils.wavelet.freq_vector_nfft
Return the frequency vector based on NFFT
pyleoclim.utils.wavelet.freq_vector_scale
Return the frequency vector based on scales
pyleoclim.utils.wavelet.freq_vector_log
Return the frequency vector based on logspace
pyleoclim.utils.wavelet.make_freq_vector
Make frequency vector
- pyleoclim.utils.wavelet.get_wwz_func(nproc, method)[source]
Return the wwz function to use.
- Parameters
nproc (int) – the number of processes for multiprocessing
method (string) – ‘Foster’ - the original WWZ method; ‘Kirchner’ - the method Kirchner adapted from Foster; ‘Kirchner_f2py’ - the method Kirchner adapted from Foster with f2py ‘Kirchner_numba’ - Kirchner’s algorithm with Numba support for acceleration (default)
- Returns
wwz_func – the wwz function to use
- Return type
function
- pyleoclim.utils.wavelet.kirchner_basic(ys, ts, freq, tau, c=0.012665147955292222, Neff_threshold=3, nproc=1, detrend=False, sg_kwargs=None, gaussianize=False, standardize=False)[source]
Return the weighted wavelet amplitude (WWA) modified by Kirchner.
Method modified by Kirchner. No multiprocessing.
- Parameters
ys (array) – a time series
ts (array) – time axis of the time series
freq (array) – vector of frequency
tau (array) – the evenly-spaced time points, namely the time shift for wavelet analysis
c (float) – the decay constant that determines the analytical resolution of frequency for analysis, the smaller the higher resolution; the default value 1/(8*np.pi**2) is good for most of the wavelet analysis cases
Neff_threshold (int) – the threshold of the number of effective degrees of freedom
nproc (int) – fake argument for convenience, for parameter consistency between functions, does not need to be specified
detrend (string) –
None - the original time series is assumed to have no trend; Types of detrending:
”linear” : the result of a linear least-squares fit to y is subtracted from y.
”constant” : only the mean of data is subtracted.
”savitzky-golay” : y is filtered using the Savitzky-Golay filter and the resulting filtered series is subtracted from y.
”emd” : Empirical mode decomposition. The last mode is assumed to be the trend and removed from the series
sg_kwargs (dict) – The parameters for the Savitzky-Golay filter. see pyleoclim.utils.filter.savitzy_golay for details.
gaussianize (bool) – If True, gaussianizes the timeseries
standardize (bool) – If True, standardizes the timeseries
- Returns
wwa (array) – the weighted wavelet amplitude
phase (array) – the weighted wavelet phase
Neffs (array) – the matrix of effective number of points in the time-scale coordinates
coeff (array) – the wavelet transform coefficients (a0, a1, a2)
References
Foster, G. Wavelets for period analysis of unevenly sampled time series. The Astronomical Journal 112, 1709 (1996).
Witt, A. & Schumann, A. Y. Holocene climate variability on millennial scales recorded in Greenland ice cores. Nonlinear Processes in Geophysics 12, 345–352 (2005).
See also
pyleoclim.utils.wavelet.wwz_basic
Returns the weighted wavelet amplitude using the original method from Kirchner. No multiprocessing
pyleoclim.utils.wavelet.wwz_nproc
Returns the weighted wavelet amplitude using the original method from Kirchner. Supports multiprocessing
pyleoclim.utils.wavelet.kirchner_nproc
Returns the weighted wavelet amplitude (WWA) modified by Kirchner. Supports multiprocessing
pyleoclim.utils.wavelet.kirchner_numba
Return the weighted wavelet amplitude (WWA) modified by Kirchner using Numba package.
pyleoclim.utils.wavelet.kirchner_f2py
Returns the weighted wavelet amplitude (WWA) modified by Kirchner. Uses Fortran. Fastest method but requires a compiler.
pyleoclim.utils.filter.savitzky_golay
Smooth (and optionally differentiate) data with a Savitzky-Golay filter.
pyleoclim.utils.tsutils.preprocess
pre-processes a times series using Gaussianization and detrending.
pyleoclim.utils.tsutils.detrend
detrending functionalities
pyleoclim.utils.tsutils.gaussianize
Quantile maps a 1D array to a Gaussian distribution
- pyleoclim.utils.wavelet.kirchner_f2py(ys, ts, freq, tau, c=0.012665147955292222, Neff_threshold=3, nproc=8, detrend=False, sg_kwargs=None, gaussianize=False, standardize=False)[source]
Returns the weighted wavelet amplitude (WWA) modified by Kirchner.
Fastest method. Calls Fortran libraries.
- Parameters
ys (array) – a time series
ts (array) – time axis of the time series
freq (array) – vector of frequency
tau (array) – the evenly-spaced time points, namely the time shift for wavelet analysis
c (float) – the decay constant that determines the analytical resolution of frequency for analysis, the smaller the higher resolution; the default value 1/(8*np.pi**2) is good for most of the wavelet analysis cases
Neff_threshold (int) – the threshold of the number of effective degrees of freedom
nproc (int) – fake argument, just for convenience
detrend (string) –
None - the original time series is assumed to have no trend; Types of detrending:
”linear” : the result of a linear least-squares fit to y is subtracted from y.
”constant” : only the mean of data is subtracted.
”savitzky-golay” : y is filtered using the Savitzky-Golay filter and the resulting filtered series is subtracted from y.
”emd” : Empirical mode decomposition. The last mode is assumed to be the trend and removed from the series
sg_kwargs (dict) – The parameters for the Savitzky-Golay filter. see pyleoclim.utils.filter.savitzy_golay for details.
gaussianize (bool) – If True, gaussianizes the timeseries
standardize (bool) – If True, standardizes the timeseries
- Returns
wwa (array) – the weighted wavelet amplitude
phase (array) – the weighted wavelet phase
Neffs (array) – the matrix of effective number of points in the time-scale coordinates
coeff (array) – the wavelet transform coefficients (a0, a1, a2)
See also
pyleoclim.utils.wavelet.wwz_basic
Returns the weighted wavelet amplitude using the original method from Kirchner. No multiprocessing
pyleoclim.utils.wavelet.wwz_nproc
Returns the weighted wavelet amplitude using the original method from Kirchner. Supports multiprocessing
pyleoclim.utils.wavelet.kirchner_basic
Return the weighted wavelet amplitude (WWA) modified by Kirchner. No multiprocessing
pyleoclim.utils.wavelet.kirchner_nproc
Returns the weighted wavelet amplitude (WWA) modified by Kirchner. Supports multiprocessing
pyleoclim.utils.wavelet.kirchner_numba
Return the weighted wavelet amplitude (WWA) modified by Kirchner using Numba package.
pyleoclim.utils.filter.savitzky_golay
Smooth (and optionally differentiate) data with a Savitzky-Golay filter.
pyleoclim.utils.tsutils.preprocess
pre-processes a times series using Gaussianization and detrending.
pyleoclim.utils.tsutils.detrend
detrending functionalities
pyleoclim.utils.tsutils.gaussianize
Quantile maps a 1D array to a Gaussian distribution
- pyleoclim.utils.wavelet.kirchner_nproc(ys, ts, freq, tau, c=0.012665147955292222, Neff_threshold=3, nproc=8, detrend=False, sg_kwargs=None, gaussianize=False, standardize=False)[source]
Return the weighted wavelet amplitude (WWA) modified by Kirchner.
Method modified by kirchner. Supports multiprocessing.
- Parameters
ys (array) – a time series
ts (array) – time axis of the time series
freq (array) – vector of frequency
tau (array) – the evenly-spaced time points, namely the time shift for wavelet analysis
c (float) – the decay constant that determines the analytical resolution of frequency for analysis, the smaller the higher resolution; the default value 1/(8*np.pi**2) is good for most of the wavelet analysis cases
Neff_threshold (int) – the threshold of the number of effective degrees of freedom
nproc (int) – the number of processes for multiprocessing
detrend (string) –
Types of detrending:
”linear” : the result of a linear least-squares fit to y is subtracted from y.
”constant” : only the mean of data is subtracted.
”savitzky-golay” : y is filtered using the Savitzky-Golay filter and the resulting filtered series is subtracted from y.
”emd” : Empirical mode decomposition. The last mode is assumed to be the trend and removed from the series
sg_kwargs (dict) – The parameters for the Savitzky-Golay filter. see pyleoclim.utils.filter.savitzy_golay for details.
gaussianize (bool) – If True, gaussianizes the timeseries
standardize (bool) – If True, standardizes the timeseries
- Returns
wwa (array) (the weighted wavelet amplitude)
phase (array) (the weighted wavelet phase)
Neffs (array) (the matrix of effective number of points in the time-scale coordinates)
coeff (array) (the wavelet transform coefficients (a0, a1, a2))
See also
pyleoclim.utils.wavelet.wwz_basic
Returns the weighted wavelet amplitude using the original method from Kirchner. No multiprocessing
pyleoclim.utils.wavelet.wwz_nproc
Returns the weighted wavelet amplitude using the original method from Kirchner. Supports multiprocessing
pyleoclim.utils.wavelet.kirchner_basic
Return the weighted wavelet amplitude (WWA) modified by Kirchner. No multiprocessing
pyleoclim.utils.wavelet.kirchner_numba
Return the weighted wavelet amplitude (WWA) modified by Kirchner using Numba package.
pyleoclim.utils.wavelet.kirchner_f2py
Returns the weighted wavelet amplitude (WWA) modified by Kirchner. Uses Fortran. Fastest method but requires a compiler.
pyleoclim.utils.filter.savitzky_golay
Smooth (and optionally differentiate) data with a Savitzky-Golay filter.
pyleoclim.utils.tsutils.preprocess
pre-processes a times series using Gaussianization and detrending.
pyleoclim.utils.tsutils.detrend
detrending functionalities
pyleoclim.utils.tsutils.gaussianize
Quantile maps a 1D array to a Gaussian distribution
- pyleoclim.utils.wavelet.kirchner_numba(ys, ts, freq, tau, c=0.012665147955292222, Neff_threshold=3, detrend=False, sg_kwargs=None, gaussianize=False, standardize=False, nproc=1)[source]
Return the weighted wavelet amplitude (WWA) modified by Kirchner.
Using numba.
- Parameters
ys (array) – a time series
ts (array) – time axis of the time series
freq (array) – vector of frequency
tau (array) – the evenly-spaced time points, namely the time shift for wavelet analysis
c (float) – the decay constant that determines the analytical resolution of frequency for analysis, the smaller the higher resolution; the default value 1/(8*np.pi**2) is good for most of the wavelet analysis cases
Neff_threshold (int) – the threshold of the number of effective degrees of freedom
nproc (int) – fake argument, just for convenience
detrend (string) –
None - the original time series is assumed to have no trend; Types of detrending:
”linear” : the result of a linear least-squares fit to y is subtracted from y.
”constant” : only the mean of data is subtracted.
”savitzky-golay” : y is filtered using the Savitzky-Golay filter and the resulting filtered series is subtracted from y.
”emd” : Empirical mode decomposition. The last mode is assumed to be the trend and removed from the series
sg_kwargs (dict) – The parameters for the Savitzky-Golay filter. see pyleoclim.utils.filter.savitzy_golay for details.
gaussianize (bool) – If True, gaussianizes the timeseries
standardize (bool) – If True, standardizes the timeseries
- Returns
wwa (array) – the weighted wavelet amplitude
phase (array) – the weighted wavelet phase
Neffs (array) – the matrix of effective number of points in the time-scale coordinates
coeff (array) – the wavelet transform coefficients (a0, a1, a2)
References
Foster, G. Wavelets for period analysis of unevenly sampled time series. The Astronomical Journal 112, 1709 (1996). Witt, A. & Schumann, A. Y. Holocene climate variability on millennial scales recorded in Greenland ice cores. Nonlinear Processes in Geophysics 12, 345–352 (2005).
See also
pyleoclim.utils.wavelet.wwz_basic
Returns the weighted wavelet amplitude using the original method from Kirchner. No multiprocessing
pyleoclim.utils.wavelet.wwz_nproc
Returns the weighted wavelet amplitude using the original method from Kirchner. Supports multiprocessing
pyleoclim.utils.wavelet.kirchner_basic
Return the weighted wavelet amplitude (WWA) modified by Kirchner. No multiprocessing
pyleoclim.utils.wavelet.kirchner_nproc
Returns the weighted wavelet amplitude (WWA) modified by Kirchner. Supports multiprocessing
pyleoclim.utils.wavelet.kirchner_f2py
Returns the weighted wavelet amplitude (WWA) modified by Kirchner. Uses Fortran. Fastest method but requires a compiler.
pyleoclim.utils.filter.savitzky_golay
Smooth (and optionally differentiate) data with a Savitzky-Golay filter.
pyleoclim.utils.tsutils.preprocess
pre-processes a times series using Gaussianization and detrending.
pyleoclim.utils.tsutils.detrend
detrending functionalities
pyleoclim.utils.tsutils.gaussianize
Quantile maps a 1D array to a Gaussian distribution
- pyleoclim.utils.wavelet.make_coi(tau, Neff_threshold=3)[source]
Return the cone of influence.
- Parameters
tau (array) – the evenly-spaced time points, namely the time shift for wavelet analysis
Neff_threshold (int) – the threshold of the number of effective samples (default: 3)
- Returns
coi – cone of influence
- Return type
array
References
wave_signif() in http://paos.colorado.edu/research/wavelets/wave_python/waveletFunctions.py
- pyleoclim.utils.wavelet.make_freq_vector(ts, method='log', **kwargs)[source]
Make frequency vector
This function selects among five methods to obtain the frequency vector.
- Parameters
ts (array) – Time axis of the time series
method (string) – The method to use. Options are ‘log’ (default), ‘nfft’, ‘lomb_scargle’, ‘welch’, and ‘scale’
kwargs (dict, optional) –
For Lomb_Scargle, additional parameters may be passed:
nf (int): number of frequency points
- ofac (float): Oversampling rate that influences the resolution of the frequency axis,
when equals to 1, it means no oversamling (should be >= 1). The default value 4 is usaually a good value.
- hifac (float): fhi/fnyq (should be >= 1), where fhi is the highest frequency that
can be analyzed by the Lomb-Scargle algorithm and fnyq is the Nyquist frequency.
- Returns
freq – the frequency vector
- Return type
array
See also
pyleoclim.utils.wavelet.freq_vector_lomb_scargle
Return the frequency vector based on the REDFIT recommendation.
pyleoclim.utils.wavelet.freq_vector_welch
Return the frequency vector based on the Welch’s method.
pyleoclim.utils.wavelet.freq_vector_nfft
Return the frequency vector based on NFFT
pyleoclim.utils.wavelet.freq_vector_scale
Return the frequency vector based on scales
pyleoclim.utils.wavelet.freq_vector_log
Return the frequency vector based on logspace
- pyleoclim.utils.wavelet.make_omega(ts, freq)[source]
Return the angular frequency based on the time axis and given frequency vector
- Parameters
ys (array) – a time series
ts (array) – time axis of the time series
freq (array) – vector of frequency
- Returns
omega – the angular frequency vector
- Return type
array
- pyleoclim.utils.wavelet.prepare_wwz(ys, ts, freq=None, freq_method='log', freq_kwargs=None, tau=None, len_bd=0, bc_mode='reflect', reflect_type='odd', **kwargs)[source]
Return the truncated time series with NaNs deleted and estimate frequency vector and tau
- Parameters
ys (array) – a time series, NaNs will be deleted automatically
ts (array) – the time points, if ys contains any NaNs, some of the time points will be deleted accordingly
freq (array) – vector of frequency. If None, will be generated according to freq_method. may be set.
freq_method (str) – when freq=None, freq will be ganerated according to freq_method
freq_kwargs (str) – used when freq=None for certain methods
tau (array) – The evenly-spaced time points, namely the time shift for wavelet analysis. If the boundaries of tau are not exactly on two of the time axis points, then tau will be adjusted to be so. If None, at most 50 tau points will be generated from the input time span.
len_bd (int) – the number of the ghost grid points desired on each boundary
bc_mode (string) – {‘constant’, ‘edge’, ‘linear_ramp’, ‘maximum’, ‘mean’, ‘median’, ‘minimum’, ‘reflect’ , ‘symmetric’, ‘wrap’} For more details, see np.lib.pad()
reflect_type (string) – {‘even’, ‘odd’}, optional Used in ‘reflect’, and ‘symmetric’. The ‘even’ style is the default with an unaltered reflection around the edge value. For the ‘odd’ style, the extented part of the array is created by subtracting the reflected values from two times the edge value. For more details, see np.lib.pad()
- Returns
ys_cut (array) – the truncated time series with NaNs deleted
ts_cut (array) – the truncated time axis of the original time series with NaNs deleted
freq (array) – vector of frequency
tau (array) – the evenly-spaced time points, namely the time shift for wavelet analysis
- pyleoclim.utils.wavelet.tc_wave_bases(mother, k, scale, param)[source]
WAVE_BASES 1D Wavelet functions Morlet, Paul, or DOG
- Parameters
mother (string) – equal to ‘MORLET’ or ‘PAUL’ or ‘DOG’
k (numpy.array) – the Fourier frequencies at which to calculate the wavelet
scale (float) – The wavelet scale
param (float) – the nondimensional parameter for the wavelet function
- Returns
daughter (numpy.array) – a vector, the wavelet function
fourier_factor (float) – the ratio of Fourier period to scale
coi (float) – the cone-of-influence size at the scale
dofmin (float) –
- degrees of freedom for each point in the wavelet power
(either 2 for Morlet and Paul, or 1 for the DOG)
References
Torrence, C. and G. P. Compo, 1998: A Practical Guide to Wavelet Analysis. Bull. Amer. Meteor. Soc., 79, 61-78. Python routines available at http://paos.colorado.edu/research/wavelets/
- pyleoclim.utils.wavelet.tc_wave_signif(ys, ts, scale, mother, param, sigtest='chi-square', qs=[0.95], dof=None, gws=None)[source]
Asymptotic singificance testing.
- Parameters
ys (numpy.array) – Values for the timeseries
ts (numpy.array) – time vector.
scale (numpy.array) – vector of scale
mother (str) – Type of mother wavelet
param (int) – mother wavelet parameter
sigtest ({'chi-square','time-average','scale-average'}, optional) –
Type of significance test to perform . The default is ‘chi-square’.
chi-square: a regular chi-square test Eq(18) from Torrence and Compo
- time-average: DOF should be set to NA, the number of local wavelet spectra that were averaged together.
For the Global Wavelet Spectrum, this would be NA=N, where N is the number of points in your time series. Eq23 in Torrence and Compo
- -scale-average: In this case, DOF should be set to a two-element vector [S1,S2], which gives the scale range that was averaged together.
e.g. if one scale-averaged scales between 2 and 8, then DOF=[2,8].
qs (list, optional) – Significance level. The default is [0.95].
dof (None, optional) –
Degrees of freedon for signif test. The default is None, which will automatically assign:
chi-square: DOF = 2 (or 1 for MOTHER=’DOG’)
time-average: DOF = NA, the number of times averaged together.
-scale-average: DOF = [S1,S2], the range of scales averaged.
gws (np.array, optional) – Global wavelet spectrum. a vector of the same length as scale. If input then this is used as the theoretical background spectrum, rather than white or red noise. The default is None.
- Returns
signif_level – Array of values for significance level
- Return type
numpy.array
References
Torrence, C. and G. P. Compo, 1998: A Practical Guide to Wavelet Analysis. Bull. Amer. Meteor. Soc., 79, 61-78. Python routines available at http://paos.colorado.edu/research/wavelets/
See also
pyleoclim.utils.wavelet.chisquare_inv
inverse of chi-square CDF
pyleoclim.utils.wavelet.chisquare_solve
return the difference between calculated percentile and true P
- pyleoclim.utils.wavelet.tc_wavelet(Y, dt, scale, mother, param, pad=False)[source]
WAVELET 1D Wavelet transform. Adapted from Torrence and Compo to fit existing Pyleoclim functionalities
Computes the wavelet transform of the vector Y (length N), with sampling rate DT.
By default, the Morlet wavelet (k0=6) is used. The wavelet basis is normalized to have total energy=1 at all scales.
- Parameters
Y (numpy.array) – the time series of length N.
dt (float) – the sampling time
mother (string, optional) – the mother wavelet function. The default is ‘MORLET’. Options are: ‘MORLET’, ‘PAUL’, or ‘DOG’
param (flaot, optional) –
the mother wavelet parameter. The default is None since it varies for each mother
For ‘MORLET’ this is k0 (wavenumber), default is 6.
For ‘PAUL’ this is m (order), default is 4.
For ‘DOG’ this is m (m-th derivative), default is 2.
pad ({True,False}, optional) – Whether or not to pad the timeseries. with zeroes to get N up to the next higher power of 2. This prevents wraparound from the end of the time series to the beginning, and also speeds up the FFT’s used to do the wavelet transform. This will not eliminate all edge effects. The default is False.
- Returns
wave (numpy.array) – The wavelet coefficients
coi (numpy.array) – The cone of influence. Periods greater than this are subject to edge effects.
See also
pyleoclim.utils.wavelet.tc_wave_bases
1D wavelet functions Morlet, Paul or Dog
References
Torrence, C. and G. P. Compo, 1998: A Practical Guide to Wavelet Analysis. Bull. Amer. Meteor. Soc., 79, 61-78. Python routines available at http://paos.colorado.edu/research/wavelets/
- pyleoclim.utils.wavelet.wtc(coeff1, coeff2, scales, tau, smooth_factor=0.25)[source]
Return the wavelet transform coherency (WTC).
- Parameters
coeff1 (array) – the first of two sets of wavelet transform coefficients in the form of a1 + a2*1j
coeff2 (array) – the second of two sets of wavelet transform coefficients in the form of a1 + a2*1j
scales (array) – vector of scales (period for WWZ; more complicated dependence for CWT)
tau (array') – the evenly-spaced time points, namely the time shift for wavelet analysis
- Returns
xw_coherence – the cross wavelet coherence
- Return type
array
References
- Grinsted, A., Moore, J. C. & Jevrejeva, S. Application of the cross wavelet transform and
wavelet coherence to geophysical time series. Nonlin. Processes Geophys. 11, 561–566 (2004).
Matlab code by Grinsted (https://github.com/grinsted/wavelet-coherence)
Python code by Sebastian Krieger (https://github.com/regeirk/pycwt)
- pyleoclim.utils.wavelet.wwa2psd(wwa, ts, Neffs, freq=None, Neff_threshold=3, anti_alias=False, avgs=2)[source]
Return the power spectral density (PSD) using the weighted wavelet amplitude (WWA).
- Parameters
wwa (array) – the weighted wavelet amplitude.
ts (array) – the time points, should be pre-truncated so that the span is exactly what is used for wwz
Neffs (array) – the matrix of effective number of points in the time-scale coordinates obtained from wwz
freq (array) – vector of frequency from wwz
Neff_threshold (int) – the threshold of the number of effective samples
anti_alias (bool) – whether to apply anti-alias filter
avgs (int) – flag for whether spectrum is derived from instantaneous point measurements (avgs<>1) OR from measurements averaged over each sampling interval (avgs==1)
- Returns
psd – power spectral density
- Return type
array
References
Kirchner’s C code for weighted psd calculation (see https://www.pnas.org/doi/full/10.1073/pnas.1304328110#supplementary-materials)
- pyleoclim.utils.wavelet.wwz(ys, ts, tau=None, ntau=None, freq=None, freq_method='log', freq_kwargs={}, c=0.012665147955292222, Neff_threshold=3, Neff_coi=3, nproc=8, detrend=False, sg_kwargs=None, method='Kirchner_numba', gaussianize=False, standardize=True, len_bd=0, bc_mode='reflect', reflect_type='odd')[source]
Weighted wavelet Z transform (WWZ) for unevenly-spaced data
- Parameters
ys (array) – a time series, NaNs will be deleted automatically
ts (array) – the time points, if ys contains any NaNs, some of the time points will be deleted accordingly
tau (array) – the evenly-spaced time vector for the analysis, namely the time shift for wavelet analysis
freq (array) – vector of frequency
freq_method (str) –
Method to generate the frequency vector if not set directly. The following options are avialable:
’log’ (default)
’lomb_scargle’
’welch’
’scale’
’nfft’
See
pyleoclim.utils.wavelet.make_freq_vector()
for detailsfreq_kwargs (str) – used when freq=None for certain methods
c (float) – the decay constant that determines the analytical resolution of frequency for analysis, the smaller the higher resolution; the default value 1/(8*np.pi**2) is good for most of the wavelet analysis cases
Neff_threshold (int) – threshold for the effective number of points
nproc (int) – the number of processes for multiprocessing
detrend (string, {None, 'linear', 'constant', 'savitzy-golay'}) –
Available methods for detrending, including
None: the original time series is assumed to have no trend;
’linear’: a linear least-squares fit to ys is subtracted;
’constant’: the mean of ys is subtracted
’savitzy-golay’: ys is filtered using the Savitzky-Golay filter and the resulting filtered series is subtracted from y.
Empirical mode decomposition. The last mode is assumed to be the trend and removed from the series
sg_kwargs (dict) – The parameters for the Savitzky-Golay filter. See
pyleoclim.utils.filter.savitzky_golay()
for details.method (string, {'Foster', 'Kirchner', 'Kirchner_f2py', 'Kirchner_numba'}) –
Available specific implementation of WWZ, including
’Foster’: the original WWZ method;
’Kirchner’: the method Kirchner adapted from Foster;
’Kirchner_f2py’: the method Kirchner adapted from Foster, implemented with f2py for acceleration;
’Kirchner_numba’: the method Kirchner adapted from Foster, implemented with Numba for acceleration (default);
len_bd (int) – the number of the ghost grids want to creat on each boundary
bc_mode (string, {'constant', 'edge', 'linear_ramp', 'maximum', 'mean', 'median', 'minimum', 'reflect' , 'symmetric', 'wrap'}) – For more details, see np.lib.pad()
reflect_type (string, optional, {‘even’, ‘odd’}) – Used in ‘reflect’, and ‘symmetric’. The ‘even’ style is the default with an unaltered reflection around the edge value. For the ‘odd’ style, the extented part of the array is created by subtracting the reflected values from two times the edge value. For more details, see np.lib.pad()
- Returns
res – a namedtuple that includes below items
- wwaarray
the weighted wavelet amplitude.
- coiarray
cone of influence
- freqarray
vector of frequency
- tauarray
the evenly-spaced time points, namely the time shift for wavelet analysis
- Neffsarray
the matrix of effective number of points in the time-scale coordinates
- coeffarray
the wavelet transform coefficients
- Return type
namedtuple
See also
pyleoclim.utils.wavelet.wwz_basic
Returns the weighted wavelet amplitude using the original method from Kirchner. No multiprocessing
pyleoclim.utils.wavelet.wwz_nproc
Returns the weighted wavelet amplitude using the original method from Kirchner. Supports multiprocessing
pyleoclim.utils.wavelet.kirchner_basic
Return the weighted wavelet amplitude (WWA) modified by Kirchner. No multiprocessing
pyleoclim.utils.wavelet.kirchner_nproc
Returns the weighted wavelet amplitude (WWA) modified by Kirchner. Supports multiprocessing
pyleoclim.utils.wavelet.kirchner_numba
Return the weighted wavelet amplitude (WWA) modified by Kirchner using Numba package.
pyleoclim.utils.wavelet.kirchner_f2py
Returns the weighted wavelet amplitude (WWA) modified by Kirchner. Uses Fortran. Fastest method but requires a compiler.
pyleoclim.utils.filter.savitzky_golay
Smooth (and optionally differentiate) data with a Savitzky-Golay filter.
pyleoclim.utils.wavelet.make_freq_vector
Make frequency vector
pyleoclim.utils.tsutils.detrend
detrending functionalities
pyleoclim.utils.tsutils.gaussianize
Quantile maps a 1D array to a Gaussian distribution
pyleoclim.utils.tsutils.preprocess
pre-processes a times series using Gaussianization and detrending.
Examples
We perform an ideal test below. We use a sine wave with a period of 50 yrs as the signal for test. Then performing wavelet analysis should return an energy band around period of 50 yrs in the scalogram.
from pyleoclim import utils import matplotlib.pyplot as plt from matplotlib.ticker import ScalarFormatter, FormatStrFormatter import numpy as np # Create a signal time = np.arange(2001) f = 1/50 # the period is then 1/f = 50 signal = np.cos(2*np.pi*f*time) # Wavelet Analysis res = utils.wwz(signal, time) # Visualization fig, ax = plt.subplots() contourf_args = {'cmap': 'magma', 'origin': 'lower', 'levels': 11} cbar_args = {'drawedges': False, 'orientation': 'vertical', 'fraction': 0.15, 'pad': 0.05} cont = ax.contourf(res.time, 1/res.freq, res.amplitude.T, **contourf_args) ax.plot(res.time, res.coi, 'k--') # plot the cone of influence ax.set_yscale('log') ax.set_yticks([2, 5, 10, 20, 50, 100, 200, 500, 1000]) ax.set_ylim([2, 1000]) ax.yaxis.set_major_formatter(ScalarFormatter()) ax.yaxis.set_major_formatter(FormatStrFormatter('%g')) ax.set_xlabel('Time (yr)') ax.set_ylabel('Period (yrs)') cb = plt.colorbar(cont, **cbar_args)
- pyleoclim.utils.wavelet.wwz_basic(ys, ts, freq, tau, c=0.012665147955292222, Neff_threshold=3, nproc=1, detrend=False, sg_kwargs=None, gaussianize=False, standardize=False)[source]
Return the weighted wavelet amplitude (WWA).
The Weighted wavelet Z-transform (WWZ) is based on Morlet wavelet estimation, using least squares minimization to suppress the energy leakage caused by data gaps. WWZ does not rely on interpolation or detrending, and is appropriate for unevenly-spaced datasets. In particular, we use the variant of Kirchner & Neal (2013), in which basis rotations mitigate the numerical instability that occurs in pathological cases with the original algorithm (Foster, 1996). The WWZ method has one adjustable parameter, a decay constant c that balances the time and frequency resolutions of the analysis. This application uses the larger value 1/(8π^2), justified elsewhere (Witt & Schumann, 2005).
No multiprocessing is applied by Default.
- Parameters
ys (array) – a time series
ts (array) – time axis of the time series
freq (array) – vector of frequency
tau (array) – the evenly-spaced time points, namely the time shift for wavelet analysis
c (float) – the decay constant that determines the analytical resolution of frequency for analysis, the smaller the higher resolution; the default value 1/(8*np.pi**2) is good for most of the wavelet analysis cases
Neff_threshold (int) – the threshold of the number of effective degrees of freedom
nproc (int) – fake argument, just for convenience
detrend (string) –
None - the original time series is assumed to have no trend (default); Types of detrending:
”linear” : the result of a linear least-squares fit to y is subtracted from y.
”constant” : only the mean of data is subtracted.
”savitzky-golay” : y is filtered using the Savitzky-Golay filter and the resulting filtered series is subtracted from y.
”emd” : Empirical mode decomposition. The last mode is assumed to be the trend and removed from the series
sg_kwargs (dict) – The parameters for the Savitzky-Golay filter. see pyleoclim.utils.filter.savitzy_golay for details.
gaussianize (bool) – If True, gaussianizes the timeseries
standardize (bool) – If True, standardizes the timeseries
- Returns
wwa (array) – the weighted wavelet amplitude
phase (array) – the weighted wavelet phase
Neffs (array) – the matrix of effective number of points in the time-scale coordinates
coeff (array) – the wavelet transform coefficients (a0, a1, a2)
References
Foster, G. Wavelets for period analysis of unevenly sampled time series. The Astronomical Journal 112, 1709 (1996).
Witt, A. & Schumann, A. Y. Holocene climate variability on millennial scales recorded in Greenland ice cores. Nonlinear Processes in Geophysics 12, 345–352 (2005).
Kirchner, J. W. and Neal, C. (2013). Universal fractal scaling in stream chemistry and its implications for solute transport and water quality trend detection. Proc Natl Acad Sci USA 110:12213–12218.
See also
pyleoclim.utils.wavelet.wwz_nproc
Returns the weighted wavelet amplitude using the original method from Kirchner. Supports multiprocessing
pyleoclim.utils.wavelet.kirchner_basic
Return the weighted wavelet amplitude (WWA) modified by Kirchner. No multiprocessing
pyleoclim.utils.wavelet.kirchner_nproc
Returns the weighted wavelet amplitude (WWA) modified by Kirchner. Supports multiprocessing
pyleoclim.utils.wavelet.kirchner_numba
Return the weighted wavelet amplitude (WWA) modified by Kirchner using Numba package.
pyleoclim.utils.wavelet.kirchner_f2py
Returns the weighted wavelet amplitude (WWA) modified by Kirchner. Uses Fortran. Fastest method but requires a compiler.
pyleoclim.utils.filter.savitzky_golay
Smooth (and optionally differentiate) data with a Savitzky-Golay filter.
pyleoclim.utils.tsutils.preprocess
pre-processes a times series using Gaussianization and detrending.
pyleoclim.utils.tsutils.detrend
detrending functionalities using 4 possible methods
pyleoclim.utils.tsutils.gaussianize
Quantile maps a 1D array to a Gaussian distribution
pyleoclim.utils.tsutils.standardize
Centers and normalizes a given time series.
- pyleoclim.utils.wavelet.wwz_coherence(ys1, ts1, ys2, ts2, smooth_factor=0.25, tau=None, freq=None, freq_method='log', freq_kwargs=None, c=0.012665147955292222, Neff_threshold=3, nproc=8, detrend=False, sg_kwargs=None, verbose=False, method='Kirchner_numba', gaussianize=False, standardize=True)[source]
Returns the wavelet coherence of two time series (WWZ method).
- Parameters
ys1 (array) – first of two time series
ys2 (array) – second of the two time series
ts1 (array) – time axis of first time series
ts2 (array) – time axis of the second time series
tau (array) – the evenly-spaced time points
freq (array) – vector of frequency
c (float) – the decay constant that determines the analytical resolution of frequency for analysis, the smaller the higher resolution; the default value 1/(8*np.pi**2) is good for most of the wavelet analysis cases
Neff_threshold (int) – threshold for the effective number of points
nproc (int) – the number of processes for multiprocessing
detrend (string) –
None: the original time series is assumed to have no trend;
’linear’: a linear least-squares fit to ys is subtracted;
’constant’: the mean of ys is subtracted
’savitzy-golay’: ys is filtered using the Savitzky-Golay filter and the resulting filtered series is subtracted from y.
Empirical mode decomposition. The last mode is assumed to be the trend and removed from the series
sg_kwargs (dict) – The parameters for the Savitzky-Golay filter. see pyleoclim.utils.filter.savitzy_golay for details.
gaussianize (bool) – If True, gaussianizes the timeseries
standardize (bool) – If True, standardizes the timeseries
method (string) –
‘Foster’: the original WWZ method;
’Kirchner’: the method Kirchner adapted from Foster;
’Kirchner_f2py’: the method Kirchner adapted from Foster with f2py
’Kirchner_numba’: Kirchner’s algorithm with Numba support for acceleration (default)
verbose (bool) – If True, print warning messages
smooth_factor (float) – smoothing factor for the WTC (default: 0.25)
- Returns
res – contains the cross wavelet coherence, cross-wavelet phase, vector of frequency, evenly-spaced time points, AR1 sims, cone of influence
- Return type
dict
References
Grinsted, A., J. C. Moore, and S. Jevrejeva (2004), Application of the cross wavelet transform and wavelet coherence to geophysical time series, Nonlinear Processes in Geophysics, 11, 561–566.
See also
pyleoclim.utils.wavelet.wwz_basic
Returns the weighted wavelet amplitude using the original method from Kirchner. No multiprocessing
pyleoclim.utils.wavelet.wwz_nproc
Returns the weighted wavelet amplitude using the original method from Kirchner. Supports multiprocessing
pyleoclim.utils.wavelet.kirchner_basic
Return the weighted wavelet amplitude (WWA) modified by Kirchner. No multiprocessing
pyleoclim.utils.wavelet.kirchner_nproc
Returns the weighted wavelet amplitude (WWA) modified by Kirchner. Supports multiprocessing
pyleoclim.utils.wavelet.kirchner_numba
Return the weighted wavelet amplitude (WWA) modified by Kirchner using Numba package.
pyleoclim.utils.wavelet.kirchner_f2py
Returns the weighted wavelet amplitude (WWA) modified by Kirchner. Uses Fortran. Fastest method but requires a compiler.
pyleoclim.utils.filter.savitzky_golay
Smooth (and optionally differentiate) data with a Savitzky-Golay filter.
pyleoclim.utils.wavelet.make_freq_vector
Make frequency vector
pyleoclim.utils.tsutils.detrend
detrending functionalities
pyleoclim.utils.tsutils.gaussianize
Quantile maps a 1D array to a Gaussian distribution
pyleoclim.utils.tsutils.preprocess
pre-processes a times series using Gaussianization and detrending.
- pyleoclim.utils.wavelet.wwz_nproc(ys, ts, freq, tau, c=0.012665147955292222, Neff_threshold=3, nproc=8, detrend=False, sg_kwargs=None, gaussianize=False, standardize=False)[source]
Return the weighted wavelet amplitude (WWA).
Original method from Foster (1996). Supports multiprocessing.
- Parameters
ys (array) – a time series
ts (array) – time axis of the time series
freq (array) – vector of frequency
tau (array) – the evenly-spaced time points, namely the time shift for wavelet analysis
c (float) – the decay constant that determines the analytical resolution of frequency for analysis, the smaller the higher resolution; the default value 1/(8*np.pi**2) is good for most of the wavelet analysis cases
Neff_threshold (int) – the threshold of the number of effective degrees of freedom [default = 3]
nproc (int) – the number of processes for multiprocessing [default = 8]
detrend (string) –
False - the original time series is assumed to have no trend; Types of detrending:
”linear” : the result of a linear least-squares fit to y is subtracted from y.
”constant” : only the mean of data is subtracted.
”savitzky-golay” : y is filtered using the Savitzky-Golay filter and the resulting filtered series is subtracted from y.
”emd” : Empirical mode decomposition. The last mode is assumed to be the trend and removed from the series
sg_kwargs (dict) – The parameters for the Savitzky-Golay filter. see pyleoclim.utils.filter.savitzy_golay for details.
gaussianize (bool) – If True, gaussianizes the timeseries
standardize (bool) – If True, standardizes the timeseries
- Returns
wwa (array) – the weighted wavelet amplitude
phase (array) – the weighted wavelet phase
Neffs (array) – the matrix of effective number of points in the time-scale coordinates
coeff (array) – the wavelet transform coefficients (a0, a1, a2)
See also
pyleoclim.utils.wavelet.wwz_basic
weighted wavelet amplitude using the original method from Kirchner. No multiprocessing
pyleoclim.utils.wavelet.kirchner_basic
weighted wavelet amplitude (WWA) modified by Kirchner. No multiprocessing
pyleoclim.utils.wavelet.kirchner_nproc
weighted wavelet amplitude (WWA) modified by Kirchner. Supports multiprocessing
pyleoclim.utils.wavelet.kirchner_numba
weighted wavelet amplitude (WWA) modified by Kirchner using Numba package.
pyleoclim.utils.wavelet.kirchner_f2py
weighted wavelet amplitude (WWA) modified by Kirchner. Uses Fortran. Fastest method but requires a compiler.
pyleoclim.utils.tsutils.preprocess
pre-processes a times series using Gaussianization and detrending.
pyleoclim.utils.filter.savitzky_golay
Smooth (and optionally differentiate) data with a Savitzky-Golay filter.
pyleoclim.utils.tsutils.detrend
detrending functionalities
pyleoclim.utils.tsutils.gaussianize
Quantile maps a 1D array to a Gaussian distribution
- pyleoclim.utils.wavelet.xwt(coeff1, coeff2)[source]
Return the cross wavelet transform.
- Parameters
coeff1 (array) – the first of two sets of wavelet transform coefficients in the form of a1 + a2*1j
coeff2 (array) – the second of two sets of wavelet transform coefficients in the form of a1 + a2*1j
freq (array) – vector of frequency
tau (array) – evenly-spaced time axis (original ttime axis for CWT, time shift for WWZ).
- Returns
xw_t (array (complex)) – the cross wavelet transform
xw_amplitude (array) – the cross wavelet amplitude
xw_phase (array) – the cross wavelet phase
References
Grinsted, A., Moore, J. C. & Jevrejeva, S. Application of the cross wavelet transform and wavelet coherence to geophysical time series. Nonlin. Processes Geophys. 11, 561–566 (2004).
Tsutils
Utilities to manipulate timeseries - useful for preprocessing prior to analysis
- pyleoclim.utils.tsutils.annualize(ys, ts)[source]
Annualize a time series whose time resolution is finer than 1 year
- Parameters
ys (array) – A time series, NaNs allowed
ts (array) – The time axis of the time series, NaNs allowed
- Returns
ys_ann (array) – the annualized time series
year_int (array) – The time axis of the annualized time series
- pyleoclim.utils.tsutils.calculate_distances(ys, n_neighbors=None, NN_kwargs=None)[source]
Uses the scikit-learn unsupervised learner for implementing neighbor searches and calculate the distance between a point and its nearest neighbors to estimate epsilon for DBSCAN.
- Parameters
ys (tnumpy.array) – the y-values for the timeseries
n_neighbors (int, optional) – Number of neighbors to use by default for kneighbors queries. The default is None.
NN_kwargs (dict, optional) – Other arguments for sklearn.neighbors.NearestNeighbors. The default is None. See: https://scikit-learn.org/stable/modules/generated/sklearn.neighbors.NearestNeighbors.html#sklearn.neighbors.NearestNeighbors
- Returns
min_eps (int) – Minimum value for epsilon.
max_eps (int) – Maximum value for epsilon.
- pyleoclim.utils.tsutils.center(y, axis=0)[source]
Centers array y (i.e. removes the sample mean)
- Parameters
y (array) – Vector of (real) numbers as a time series, NaNs allowed
axis (int or None) – Axis along which to operate, if None, compute over the whole array
- Returns
yc (array) – The centered time series, yc = (y - ybar), NaNs allowed
ybar (real) – The sampled mean of the original time series, y
References
Tapio Schneider’s MATLAB code: https://github.com/tapios/RegEM/blob/master/center.m
- pyleoclim.utils.tsutils.detect_outliers_DBSCAN(ys, nbr_clusters=None, eps=None, min_samples=None, n_neighbors=None, metric='euclidean', NN_kwargs=None, DBSCAN_kwargs=None)[source]
Uses the unsupervised learning DBSCAN algorithm to identify outliers in timeseries data. The algorithm uses the silhouette score calculated over a range of epsilon and minimum sample values to determine the best clustering. In this case, we take the largest silhouette score (as close to 1 as possible).
The DBSCAN implementation used here is from scikit-learn: https://scikit-learn.org/stable/modules/generated/sklearn.cluster.DBSCAN.html
The Silhouette Coefficient is calculated using the mean intra-cluster distance (a) and the mean nearest-cluster distance (b) for each sample. The best value is 1 and the worst value is -1. Values near 0 indicate overlapping clusters. Negative values generally indicate that a sample has been assigned to the wrong cluster, as a different cluster is more similar. For additional details, see: https://scikit-learn.org/stable/modules/generated/sklearn.metrics.silhouette_score.html
- Parameters
ys (numpy.array) – The y-values for the timeseries data.
nbr_clusters (int, optional) – Number of clusters. Note that the DBSCAN algorithm calculates the number of clusters automatically. This paramater affects the optimization over the silhouette score. The default is None.
eps (float or list, optional) – epsilon. The default is None, which allows the algorithm to optimize for the best value of eps, using the silhouette score as the optimization criterion. The maximum distance between two samples for one to be considered as in the neighborhood of the other. This is not a maximum bound on the distances of points within a cluster. This is the most important DBSCAN parameter to choose appropriately for your data set and distance function.
min_samples (int or list, optional) – The number of samples (or total weight) in a neighborhood for a point to be considered as a core point. This includes the point itself.. The default is None and optimized using the silhouette score
n_neighbors (int, optional) – Number of neighbors to use by default for kneighbors queries, which can be used to calculate a range of plausible eps values. The default is None.
metric (str, optional) – The metric to use when calculating distance between instances in a feature array. The default is ‘euclidean’. See https://scikit-learn.org/stable/modules/generated/sklearn.cluster.DBSCAN.html for alternative values.
NN_kwargs (dict, optional) – Other arguments for sklearn.neighbors.NearestNeighbors. The default is None. See: https://scikit-learn.org/stable/modules/generated/sklearn.neighbors.NearestNeighbors.html#sklearn.neighbors.NearestNeighbors
DBSCAN_kwargs (dict, optional) – Other arguments for sklearn.cluster.DBSCAN. The default is None. See: https://scikit-learn.org/stable/modules/generated/sklearn.cluster.DBSCAN.html
- Returns
indices (list) – list of indices that are considered outliers.
res (pandas.DataFrame) – Results of the clustering analysis. Contains information about eps value, min_samples value, number of clusters, the silhouette score, the indices of the outliers for each combination, and the cluster assignment for each point.
- pyleoclim.utils.tsutils.detect_outliers_kmeans(ys, nbr_clusters=None, max_cluster=10, threshold=3, kmeans_kwargs=None)[source]
Outlier detection using the unsupervised alogrithm kmeans. The algorithm runs through various number of clusters and optimizes based on the silhouette score.
KMeans implementation: https://scikit-learn.org/stable/modules/generated/sklearn.cluster.KMeans.html
The Silhouette Coefficient is calculated using the mean intra-cluster distance (a) and the mean nearest-cluster distance (b) for each sample. The best value is 1 and the worst value is -1. Values near 0 indicate overlapping clusters. Negative values generally indicate that a sample has been assigned to the wrong cluster, as a different cluster is more similar. For additional details, see: https://scikit-learn.org/stable/modules/generated/sklearn.metrics.silhouette_score.html
- Parameters
ys (numpy.array) – The y-values for the timeseries data
nbr_clusters (int or list, optional) – A user number of clusters to considered. The default is None.
max_cluster (int, optional) – The maximum number of clusters to consider in the optimization based on the Silhouette Score. The default is 10.
threshold (int, optional) – The algorithm uses the suclidean distance for each point in the cluster to identify the outliers. This parameter sets the threshold on the euclidean distance to define an outlier. The default is 3.
kmeans_kwargs (dict, optional) – Other parameters for the kmeans function. See: https://scikit-learn.org/stable/modules/generated/sklearn.cluster.KMeans.html for details. The default is None.
- Returns
indices (list) – list of indices that are considered outliers.
res (pandas.DataFrame) – Results of the clustering analysis. Contains information about number of clusters, the silhouette score, the indices of the outliers for each combination, and the cluster assignment for each point.
- pyleoclim.utils.tsutils.detrend(y, x=None, method='emd', n=1, preserve_mean=False, sg_kwargs=None)[source]
Detrend a timeseries according to four methods
Detrending methods include: “linear”, “constant”, using a low-pass Savitzky-Golay filter, and Empirical Mode Decomposition (default). Linear and constant methods use scipy.signal.detrend., EMD uses pyhht.emd.EMD.
- Parameters
y (array) – The series to be detrended.
x (array) – Abscissa for array y. Necessary for use with the Savitzky-Golay method, since the series should be evenly spaced.
method (str) –
The type of detrending:
”linear”: the result of a linear least-squares fit to y is subtracted from y.
”constant”: only the mean of data is subtracted.
”savitzky-golay”, y is filtered using the Savitzky-Golay filters and the resulting filtered series is subtracted from y.
”emd” (default): Empirical mode decomposition. The last mode is assumed to be the trend and removed from the series
n (int) – Works only if method == ‘emd’. The number of smoothest modes to remove.
preserve_mean (boolean) – flag to indicate whether the mean of the series should be preserved despite the detrending
sg_kwargs (dict) – The parameters for the Savitzky-Golay filters.
- Returns
ys (array) – The detrended version of y.
trend (array) – The removed trend. Only non-empty for EMD and Savitzy-Golay methods, since SciPy detrending does not retain the trends
See also
pyleoclim.utils.filter.savitzky_golay
Filtering using Savitzy-Golay
pyleoclim.utils.tsutils.preprocess
pre-processes a times series using standardization and detrending.
- pyleoclim.utils.tsutils.eff_sample_size(y, detrend_flag=False)[source]
Effective Sample Size of timeseries y
- Parameters
y (float) – 1d array
detrend_flag (boolean) – if True (default), detrends y before estimation.
- Returns
neff – The effective sample size
- Return type
float
References
Thiébaux HJ and Zwiers FW, 1984: The interpretation and estimation of effective sample sizes. Journal of Climate and Applied Meteorology 23: 800–811.
- pyleoclim.utils.tsutils.gauss(ys)
Maps a 1D array to a Gaussian distribution using the inverse Rosenblatt transform
The resulting array is mapped to a standard normal distribution, and therefore has zero mean and unit standard deviation. Using gaussianize() obviates the need for standardize().
- Parameters
ys (1D Array) – e.g. a timeseries
- Returns
yg – Gaussianized values of ys.
- Return type
1D Array
References
- van Albada, S., and P. Robinson (2007), Transformation of arbitrary
distributions to the normal distribution with application to EEG test-retest reliability, Journal of Neuroscience Methods, 161(2), 205 - 211, doi:10.1016/j.jneumeth.2006.11.004.
See also
pyleoclim.utils.tsutils.standardize
Centers and normalizes a time series
- pyleoclim.utils.tsutils.gaussianize(ys)[source]
Maps a 1D array to a Gaussian distribution using the inverse Rosenblatt transform
The resulting array is mapped to a standard normal distribution, and therefore has zero mean and unit standard deviation. Using gaussianize() obviates the need for standardize().
- Parameters
ys (1D Array) – e.g. a timeseries
- Returns
yg – Gaussianized values of ys.
- Return type
1D Array
References
- van Albada, S., and P. Robinson (2007), Transformation of arbitrary
distributions to the normal distribution with application to EEG test-retest reliability, Journal of Neuroscience Methods, 161(2), 205 - 211, doi:10.1016/j.jneumeth.2006.11.004.
See also
pyleoclim.utils.tsutils.standardize
Centers and normalizes a time series
- pyleoclim.utils.tsutils.gkernel(t, y, h=3.0, step=None, start=None, stop=None, step_style=None, evenly_spaced=False, bin_edges=None, time_axis=None, no_nans=True)[source]
Coarsen time resolution using a Gaussian kernel
The behavior of bins, as defined either by start, stop and step (or step_style) or by the bins argument, is to have all bins except the last one be half open. That is if bins are defined as bins = [1,2,3,4], bins will be [1,2), [2,3), [3,4]. This is the default behaviour of our binning functionality (upon which this function is based).
- Parameters
t (1d array) – the original time axis
y (1d array) – values on the original time axis
h (float) – kernel e-folding scale
step (float) – The interpolation step. Default is max spacing between consecutive points.
start (float) – where/when to start the interpolation. Default is min(t).
stop (float) – where/when to stop the interpolation. Default is max(t).
step_style (str) – step style to be applied from ‘increments’ [default = ‘max’]
evenly_spaced ({True,False}) – Makes the series evenly-spaced. This option is ignored if bins are passed. This option is being deprecated, no_nans should be used instead.
bin_edges (array) – The right hand edge of bins to use for binning. E.g. if bins = [1,2,3,4], bins will be [1,2), [2,3), [3,4]. Same behavior as scipy.stats.binned_statistic Start, stop, step, and step_style will be ignored if this is passed.
time_axis (np.ndarray) – The time axis to use for binning. If passed, bin_edges will be set as the midpoints between times. The first time will be used as the left most edge, the last time will be used as the right most edge. Start, stop, bin_size, and step_style will be ignored if this is passed.
no_nans (bool; {True,False}) – Sets the step_style to max, ensuring that the resulting series contains no empty values (nans). Default is True.
- Returns
tc (1d array) – the coarse-grained time axis
yc (1d array) – The coarse-grained time series
Notes
start, stop, step, and step_style are interpreted as defining the bin_edges for this function. This differs from the interp interpretation, which uses these to define the time axis over which interpolation is applied. For gkernel, the time axis will be specified as the midpoints between bin_edges, unless time_axis is explicitly passed.
References
Rehfeld, K., Marwan, N., Heitzig, J., and Kurths, J.: Comparison of correlation analysis techniques for irregularly sampled time series, Nonlin. Processes Geophys., 18, 389–404, doi:10.5194/npg-18-389-2011, 2011.
See also
pyleoclim.utils.tsutils.increments
Establishes the increments of a numerical array
pyleoclim.utils.tsutils.make_even_axis
Create an even time axis
pyleoclim.utils.tsutils.bin
Bin the values
pyleoclim.utils.tsutils.interp
Interpolate y onto a new x-axis
Examples
There are several ways to specify the way coarsening is done via this function. Within these there is a hierarchy which we demonstrate below.
Top priority is given to bin_edges if it is not None. All other arguments will be ignored (except for x and y). The resulting time axis will be comprised of the midpoints between bin edges.
import numpy as np import pyleoclim as pyleo x = np.array([1,2,3,5,8,12,20]) y = np.ones(len(x)) xc,yc = pyleo.utils.tsutils.gkernel(x,y,bin_edges=[1,4,8,12,16,20]) xc
array([ 2.5, 6. , 10. , 14. , 18. ])
Next, priority will go to time_axis if it is passed. In this case, bin edges will be taken as the midpoints between time axis points. The first and last time point will be used as the left most and right most bin edges.
x = np.array([1,2,3,5,8,12,20]) y = np.ones(len(x)) xc,yc = pyleo.utils.tsutils.gkernel(x,y,time_axis=[1,4,8,12,16,20]) xc
array([ 1, 4, 8, 12, 16, 20])
If time_axis is None, step will be considered, overriding step_style if it is passed. start and stop will be generated using defaults if not passed.
x = np.array([1,2,3,5,8,12,20]) y = np.ones(len(x)) xc,yc = pyleo.utils.tsutils.gkernel(x,y,step=2) xc
array([ 2., 4., 6., 8., 10., 12., 14., 16., 18.])
If both time_axis and step are None but step_style is specified, the step will be generated using the prescribed step_style.
x = np.array([1,2,3,5,8,12,20]) y = np.ones(len(x)) xc,yc = pyleo.utils.tsutils.gkernel(x,y,step_style='max') xc
array([ 5., 13.])
If none of these are specified, the mean spacing will be used.
x = np.array([1,2,3,5,8,12,20]) y = np.ones(len(x)) xc,yc = pyleo.utils.tsutils.gkernel(x,y) xc
array([ 5., 13.])
- pyleoclim.utils.tsutils.increments(x, step_style='median')[source]
Establishes the increments of a numerical array: start, stop, and representative step.
- Parameters
x (array) –
step_style (str) –
Method to obtain a representative step if x is not evenly spaced. Valid entries: ‘median’ [default], ‘mean’, ‘mode’ or ‘max’ The mode is the most frequent entry in a dataset, and may be a good choice if the timeseries is nearly equally spaced but for a few gaps.
Max is a conservative choice, appropriate for binning methods and Gaussian kernel coarse-graining
- Returns
start (float) – min(x)
stop (float) – max(x)
step (float) – The representative spacing between consecutive values, computed as above
See also
pyleoclim.utils.tsutils.bin
Bin the values
pyleoclim.utils.tsutils.gkernel
Coarsen time resolution using a Gaussian kernel
- pyleoclim.utils.tsutils.interp(x, y, interp_type='linear', step=None, start=None, stop=None, step_style=None, time_axis=None, **kwargs)[source]
Interpolate y onto a new x-axis
Largely a wrapper for scipy.interpolate.interp1d.
- Parameters
x (array) – The x-axis
y (array) – The y-axis
interp_type (str) – Options include: ‘linear’, ‘nearest’, ‘zero’, ‘slinear’, ‘quadratic’, ‘cubic’, ‘previous’, ‘next’ where ‘zero’, ‘slinear’, ‘quadratic’ and ‘cubic’ refer to a spline interpolation of zeroth, first, second or third order; ‘previous’ and ‘next’ simply return the previous or next value of the point) or as an integer specifying the order of the spline interpolator to use. Default is ‘linear’.
step (float) – The interpolation step. Default is mean spacing between consecutive points. Step_style will be ignored if this is passed.
start (float) – Where/when to start the interpolation. Default is the minimum.
stop (float) – Where/when to stop the interpolation. Default is the maximum.
step_style (str; {'min','mean','median','max'}) – Step style to use when determining the size of the interval between points. Default is None.
time_axis (np.ndarray) – Time axis onto which the series will be interpolated. Start, stop, step, and step_style will be ignored if this is passed
kwargs (kwargs) – Aguments specific to interpolate.interp1D. If getting an error about extrapolation, you can use the arguments bound_errors=False and fill_value=”extrapolate” to allow for extrapolation.
- Returns
xi (array) – The interpolated x-axis
yi (array) – The interpolated y values
Notes
start, stop, step and step_styl`e pertain to the creation of the time axis over which interpolation will be conducted. This differs from the way that the functions `bin and gkernel interpret these arguments, which is as defining the bin_edges parameter used in those functions.
See also
pyleoclim.utils.tsutils.increments
Establishes the increments of a numerical array
pyleoclim.utils.tsutils.make_even_axis
Makes an evenly spaced time axis
pyleoclim.utils.tsutils.bin
Bin the values
pyleoclim.utils.tsutils.gkernel
Coarsen time resolution using a Gaussian kernel
Examples
There are several ways to specifiy a time axis for interpolation. Within these there is a hierarchy which we demonstrate below.
Top priority will always go to time_axis if it is passed. All other arguments will be overwritten (except for x,y, and interp_type).
import numpy as np import pyleoclim as pyleo x = np.array([1,2,3,5,8,12,20]) y = np.ones(len(x)) xi,yi = pyleo.utils.tsutils.interp(x,y,time_axis=[1,4,8,12,16]) xi
array([ 1, 4, 8, 12, 16])
If time_axis is None, step will be considered, overriding step_style if it is passed. `start and stop will be generated using defaults if not passed.
x = np.array([1,2,3,5,8,12,20]) y = np.ones(len(x)) xi,yi = pyleo.utils.tsutils.interp(x,y,step=2) xi
array([ 1., 3., 5., 7., 9., 11., 13., 15., 17., 19.])
If both time_axis and step are None but step_style is specified, the step will be generated using the prescribed step_style.
x = np.array([1,2,3,5,8,12,20]) y = np.ones(len(x)) xi,yi = pyleo.utils.tsutils.interp(x,y,step_style='max') xi
array([ 1., 9., 17.])
If none of these are specified, the mean spacing will be used.
x = np.array([1,2,3,5,8,12,20]) y = np.ones(len(x)) xi,yi = pyleo.utils.tsutils.interp(x,y) xi
array([ 1. , 4.16666667, 7.33333333, 10.5 , 13.66666667, 16.83333333, 20. ])
- pyleoclim.utils.tsutils.make_even_axis(x=None, start=None, stop=None, step=None, step_style=None, no_nans=False)[source]
Create a uniform time axis for binning/interpolating
- Parameters
x (np.ndarray) – Uneven time axis upon which to base the uniform time axis.
start (float) – Where to start the axis. Default is the first value of the passed time axis.
stop (float) – Where to stop the axis. Default is the last of value of the passed time axis.
step (float) – The step size to use for the axis. Must be greater than 0.
step_style (str; {}) – Step style to use when defining the step size. Will be overridden by step if it is passed.
no_nans (bool: {True,False}) – Whether or not to allow nans. When True, will set step style to ‘max’. Will be overridden by step_style or step if they are passed. Default is False.
------- –
time_axis (np.ndarray) – An evenly spaced time axis.
- pyleoclim.utils.tsutils.preprocess(ys, ts, detrend=False, sg_kwargs=None, gaussianize=False, standardize=True)[source]
Return the processed time series using detrend and standardization.
- Parameters
ys (array) – a time series
ts (array) – The time axis for the timeseries. Necessary for use with the Savitzky-Golay filters method since the series should be evenly spaced.
detrend (string) – ‘none’/False/None - no detrending will be applied; ‘emd’ - the last mode is assumed to be the trend and removed from the series ‘linear’ - a linear least-squares fit to ys is subtracted; ‘constant’ - the mean of ys is subtracted ‘savitzy-golay’ - ys is filtered using the Savitzky-Golay filter and the resulting filtered series is subtracted.
sg_kwargs (dict) – The parameters for the Savitzky-Golay filter.
gaussianize (bool) – If True, gaussianizes the timeseries
standardize (bool) – If True, standardizes the timeseries
- Returns
res – the processed time series
- Return type
array
See also
pyleoclim.utils.tsutils.detrend
Detrend a timeseries according to four methods
pyleoclim.utils.filter.savitzy_golay
Filtering using Savitzy-Golay method
pyleoclim.utils.tsutils.standardize
Centers and normalizes a given time series
pyleoclim.utils.tsutils.gaussianize
Quantile maps a matrix to a Gaussian distribution
- pyleoclim.utils.tsutils.remove_outliers(ts, ys, indices)[source]
Remove the outliers from timeseries data
- Parameters
ts (numpy.array) – The time axis for the timeseries data.
ys (numpy.array) – The y-values for the timeseries data.
indices (numpy.array) – The indices of the outliers to be removed.
- Returns
ys (numpy.array) – The time axis for the timeseries data after outliers removal
ts (numpy.array) – The y-values for the timeseries data after outliers removal
- pyleoclim.utils.tsutils.simple_stats(y, axis=None)[source]
Computes simple statistics
Computes the mean, median, min, max, standard deviation, and interquartile range of a numpy array y, ignoring NaNs.
- Parameters
y (array) – A Numpy array
axis (int, tuple of ints) – Axis or Axes along which the means are computed, the default is to compute the mean of the flattened array. If a tuple of ints, performed over multiple axes
- Returns
mean (float) – mean of y, ignoring NaNs
median (float) – median of y, ignoring NaNs
min_ (float) – mininum value in y, ignoring NaNs
max_ (float) – max value in y, ignoring NaNs
std (float) – standard deviation of y, ignoring NaNs
IQR (float) – Interquartile range of y along specified axis, ignoring NaNs
- pyleoclim.utils.tsutils.standardize(x, scale=1, axis=0, ddof=0, eps=0.001)[source]
Centers and normalizes a time series. Constant or nearly constant time series not rescaled.
- Parameters
x (array) – vector of (real) numbers as a time series, NaNs allowed
scale (real) – A scale factor used to scale a record to a match a given variance
axis (int or None) – axis along which to operate, if None, compute over the whole array
ddof (int) – degress of freedom correction in the calculation of the standard deviation
eps (real) – a threshold to determine if the standard deviation is too close to zero
- Returns
z (array) – The standardized time series (z-score), Z = (X - E[X])/std(X)*scale, NaNs allowed
mu (real) – The mean of the original time series, E[X]
sig (real) – The standard deviation of the original time series, std[X]
References
Tapio Schneider’s MATLAB code: https://github.com/tapios/RegEM/blob/master/standardize.m
The zscore function in SciPy: https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.zscore.html
See also
pyleoclim.utils.tsutils.preprocess
pre-processes a times series using standardization and detrending.
- pyleoclim.utils.tsutils.std(x, scale=1, axis=0, ddof=0, eps=0.001)
Centers and normalizes a time series. Constant or nearly constant time series not rescaled.
- Parameters
x (array) – vector of (real) numbers as a time series, NaNs allowed
scale (real) – A scale factor used to scale a record to a match a given variance
axis (int or None) – axis along which to operate, if None, compute over the whole array
ddof (int) – degress of freedom correction in the calculation of the standard deviation
eps (real) – a threshold to determine if the standard deviation is too close to zero
- Returns
z (array) – The standardized time series (z-score), Z = (X - E[X])/std(X)*scale, NaNs allowed
mu (real) – The mean of the original time series, E[X]
sig (real) – The standard deviation of the original time series, std[X]
References
Tapio Schneider’s MATLAB code: https://github.com/tapios/RegEM/blob/master/standardize.m
The zscore function in SciPy: https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.zscore.html
See also
pyleoclim.utils.tsutils.preprocess
pre-processes a times series using standardization and detrending.
- pyleoclim.utils.tsutils.ts2segments(ys, ts, factor=10)[source]
Chop a time series into several segments based on gap detection.
- The rule of gap detection is very simple:
we define the intervals between time points as dts, then if dts[i] is larger than factor * dts[i-1], we think that the change of dts (or the gradient) is too large, and we regard it as a breaking point and chop the time series into two segments here
- Parameters
ys (array) – A time series, NaNs allowed
ts (array) – The time points
factor (float) – The factor that adjusts the threshold for gap detection
- Returns
seg_ys (list) – A list of several segments with potentially different lengths
seg_ts (list) – A list of the time axis of the several segments
n_segs (int) – The number of segments
Tsbase
Basic functionalities to clean timeseries data prior to analysis
- pyleoclim.utils.tsbase.clean_ts(ys, ts, verbose=False)[source]
Cleaning the timeseries
Delete the NaNs in the time series and sort it with time axis ascending, duplicate timestamps will be reduced by averaging the values.
- Parameters
ys (array) – A time series, NaNs allowed
ts (array) – The time axis of the time series, NaNs allowed
verbose (bool) – If True, will print a warning message
- Returns
ys (array) – The time series without nans
ts (array) – The time axis of the time series without nans
See also
pyleoclim.utils.tsbase.dropna
Drop NaN values
pyleoclim.utils.tsbase.sort_ts
Sort timeseries
pyleoclim.utils.tsbase.reduce_duplicated_timestamps
Consolidate duplicated timestamps
- pyleoclim.utils.tsbase.convert_datetime_index_to_time(datetime_index, time_unit, time_name)[source]
Convert a Pandas DatetimeIndex into a numpy array of floats.
The general formula is:
datetime_index = datum +/- time*10**exponent
where we assume
time
to use the Gregorian calendar. If dealing with other calendars, then conversions need to happen before reaching pyleoclim.- Parameters
datetime_index (pd.DatetimeIndex) – Index to covert to floats
time_unit (str) – Time unit indicates the major unit of time. Examples: annum (yr), kiloyear (ka, ky), milayear (ma, my), gigayear (ga, gy)
time_name (str) – If ‘age’, direction is always ‘retrograde’.
- Return type
np.array((float,)) of converted times
Examples
from pyleoclim.utils.tsbase import convert_datetime_index_to_time import pandas as pd import numpy as np time_unit = 'ga' time_name = None dti = pd.date_range("2018-01-01", periods=5, freq="Y", unit='s') df = pd.DataFrame(np.array(range(5)), index=dti) time = convert_datetime_index_to_time( df.index, time_unit, time_name=time_name, ) print(np.array(time))
[-6.89980514e-08 -6.99973883e-08 -7.09994631e-08 -7.19987999e-08 -7.29981368e-08]
- pyleoclim.utils.tsbase.disambiguate_time_metadata(time_unit)[source]
Infer time_name and time_unit from (possibly ambiguous) time units as commonly provided in the field.
- Parameters
time_unit (str) – time units, preferaby something like “kyr BP” or ‘year C.E.’. Otherwise, wild guesses will be attempted to decipher your meaning.
- Returns
time_name (str) – Name of the time vector (e.g., ‘Time’,’Age’). Possibly None if no guess could be made
time_unit (str) – Updated units for the time vector (e.g., ‘ky BP’).
- pyleoclim.utils.tsbase.is_evenly_spaced(x, tol=0.0001)[source]
Check if an axis x is evenly spaced, within a given tolerance
- Parameters
x (array) –
tol (float64) – Numerical tolerance for the relative difference
- Returns
check – True - evenly spaced; False - unevenly spaced.
- Return type
bool
- pyleoclim.utils.tsbase.reduce_duplicated_timestamps(ys, ts, verbose=False)[source]
Consolidate duplicated timestamps
Reduce duplicated timestamps in a timeseries by averaging the values
- Parameters
ys (array) – Dependent variable
ts (array) – Independent variable
verbose (bool) – If True, will print a warning message
- Returns
ys (array) – Dependent variable
ts (array) – Independent variable, with duplicated timestamps reduced by averaging the values
- pyleoclim.utils.tsbase.sort_ts(ys, ts, ascending=True, verbose=False)[source]
Sort timeseries
- Parameters
ys (array) – Dependent variable
ts (array) – Independent variable
verbose (bool) – If True, will print a warning message
- Returns
ys (array) – Dependent variable
ts (array) – Independent variable, sorted in ascending order
- pyleoclim.utils.tsbase.time_to_datetime(time, datum=0, exponent=0, direction='prograde', unit='s')[source]
Converts a vector of time values to a pandas datetime object
The general formula is:
datetime_index = datum +/- time*10**exponent
where we assume
time
to use the Gregorian calendar. If dealing with other calendars, then conversions need to happen before reaching pyleoclim.- Parameters
time (array-like) – the time axis to be converted
datum (int, optional) – origin point for the time scale. The default is 0.
exponent (int, optional) – Base-10 exponent for year multiplier. Dates in kyr should use 3, dates in Myr should use 6, etc. The default is 0.
direction (str, optional) – Direction of time flow, ‘prograde’ [default] or ‘retrograde’.
unit (str, optional) – Units of the datetime. Default is ‘s’, corresponding to seconds. Only change if you have an excellent reason to use finer resolution!
- Return type
index, a datetime64[unit] object
- pyleoclim.utils.tsbase.time_unit_to_datum_exp_dir(time_unit, time_name=None, verbose=False)[source]
Convert time unit (yr, ka, ma, etc) to a datum, exponent, direction triplet. Based on the time_unit (and optionally, the time_name) the datum (year zero), exponent (10^x year units), and direction (prograde/retrograde) can be inferred. A verbose option is included here for users who want to confirm the resulting inference.
- Parameters
time_unit (str) – Time unit indicates the major unit of time. Examples: annum (yr), kiloyear (ka, ky), milayear (ma, my), gigayear (ga, gy)
time_name (str) – (Optional) If ‘age’, direction is always ‘retrograde’. Defaults to None, which is effectively unused.
verbose (bool) – (Optional) If True, includes a print statement explaining the conversion.
- Returns
datum (int, optional) – origin point for the time scale.
exponent (int, optional) – Base-10 exponent for year multiplier. Dates in kyr should use 3, dates in Myr should use 6, etc.
direction (str) – Direction of time flow, ‘prograde’ or ‘retrograde’.
Examples
from pyleoclim.utils.tsbase import time_unit_to_datum_exp_dir (datum, exponent, direction) = time_unit_to_datum_exp_dir(time_unit) (datum, exponent, direction)
(1950, 9, 'retrograde')
Lipdutils
Utilities to manipulate LiPD files and automate data transformation whenever possible. These functions are used throughout Pyleoclim but are not meant for direct interaction by users. Also handles integration with the LinkedEarth wiki and the LinkedEarth Ontology.
- pyleoclim.utils.lipdutils.LipdToOntology(archiveType)[source]
standardize archiveType
Transform the archiveType from their LiPD name to their ontology counterpart
- Parameters
archiveType (string) – name of the archiveType from the LiPD file
- Returns
archiveType – archiveType according to the ontology
- Return type
string
- pyleoclim.utils.lipdutils.PLOT_DEFAULT = {'coral': ['#FF8B00', 'o'], 'documents': ['k', 'p'], 'glacierice': ['#86CDFA', 'd'], 'hybrid': ['#00BEFF', '*'], 'ice-other': ['#FFD600', 'h'], 'ice/rock': ['#FFD600', 'h'], 'instrumental': ['#8f21d8', '*'], 'lakesediment': ['#4169E0', 's'], 'marinesediment': ['#8A4513', 's'], 'midden': ['#824E2B', 'o'], 'model': ['#b4a7d6', 'd'], 'molluskshells': ['#FFD600', 'h'], 'other': ['k', 'o'], 'peat': ['#2F4F4F', '*'], 'sclerosponge': ['r', 'o'], 'speleothem': ['#FF1492', 'd'], 'wood': ['#32CC32', '^']}
The following functions handle the LiPD files
- pyleoclim.utils.lipdutils.checkTimeAxis(timeseries, x_axis=None)[source]
This function makes sure that time is available for the timeseries
- Parameters
timeseries (dict) – A LiPD timeseries object
- Returns
x (array) – the time values for the timeseries
label (string) – the time representation for the timeseries
- pyleoclim.utils.lipdutils.checkXaxis(timeseries, x_axis=None)[source]
Check that a x-axis is present for the timeseries
- Parameters
timeseries (dict) – a timeseries
x_axis (string) – the x-axis representation, either depth, age or year
- Returns
x (array) – the values for the x-axis representation
label (string) – returns either “age”, “year”, or “depth”
- pyleoclim.utils.lipdutils.enumerateLipds(lipds)[source]
Enumerate the LiPD files loaded in the workspace
- Parameters
lipds (dict) – A dictionary of LiPD files.
- pyleoclim.utils.lipdutils.enumerateTs(timeseries_list)[source]
Enumerate the available time series objects
- Parameters
timeseries_list (list) – a list of available timeseries objects.
- pyleoclim.utils.lipdutils.gen_dict_extract(key, var)[source]
Recursively searches for all the values in nested dictionaries corresponding to a particular key
- Parameters
key (str) – The key to search for
var (dict) – The dictionary to search
- pyleoclim.utils.lipdutils.getEnsemble(csv_dict, csvName)[source]
Extracts the ensemble values and depth vector from the dictionary and returns them into two numpy arrays.
- Parameters
csv_dict (dict) – dictionary containing the availableTables
csvName (str) – Name of the csv
- Returns
depth (array) – Vector of depth
ensembleValues (array) – The matrix of Ensemble values
- pyleoclim.utils.lipdutils.getLipd(lipds)[source]
Prompt for a LiPD file
Ask the user to select a LiPD file from a list Use this function in conjunction with enumerateLipds()
- Parameters
lipds (dict) – A dictionary of LiPD files. Can be obtained from pyleoclim.readLipd()
- Returns
select_lipd – The index of the LiPD file
- Return type
int
- pyleoclim.utils.lipdutils.getMeasurement(csvName, lipd)[source]
Extract the dictionary corresponding to the measurement table
- Parameters
csvName (string) – The name of the csv file
lipd (dict) – The LiPD object from which to extract the data
- Returns
ts_list – A dictionary containing data and metadata for each column in the csv file.
- Return type
dict
- pyleoclim.utils.lipdutils.getTs(timeseries_list, option=None)[source]
Get a specific timeseries object from a dictionary of timeseries
- Parameters
timeseries_list (list) – a list of available timeseries objects.
option (string) – An expression to filter the datasets. Uses lipd.filterTs()
- Returns
timeseries – A single timeseries object if not optional filter selected or a filtered list if optional arguments given
- Return type
single timeseries object or list of timeseries
See also
pyleoclim.utils.lipdutils.enumerateTs
Enumerate the available time series objects
pyleoclim.utils.lipdutils.promptForVariable
Prompt for a specific variable
- pyleoclim.utils.lipdutils.isEnsemble(csv_dict)[source]
Check whether ensembles are available
- Parameters
csv_dict (dict) – Dictionary of available csv
- Returns
paleoEnsembleTables (list) – List of available paleoEnsembleTables
chronEnsembleTables (list) – List of availale chronEnsemble Tables
- pyleoclim.utils.lipdutils.isMeasurement(csv_dict)[source]
Check whether measurement tables are available
- Parameters
csv_dict (dict) – Dictionary of available csv
- Returns
paleoMeasurementTables (list) – List of available paleoMeasurementTables
chronMeasurementTables (list) – List of available chronMeasurementTables
- pyleoclim.utils.lipdutils.isModel(csvName, lipd)[source]
Check for the presence of a model in the same object as the measurement table
- Parameters
csvName (string) – The name of the csv file corresponding to the measurement table
lipd (dict) – A LiPD object
- Returns
model (list) – List of models already available
dataObject (string) – The name of the paleoData or ChronData object in which the model(s) are stored
- pyleoclim.utils.lipdutils.mapAgeEnsembleToPaleoData(ensembleValues, depthEnsemble, depthPaleo)[source]
Map the depth for the ensemble age values to the paleo depth
- Parameters
ensembleValues (array) – A matrix of possible age models. Realizations should be stored in columns
depthEnsemble (array) – A vector of depth. The vector should have the same length as the number of rows in the ensembleValues
depthPaleo (array) – A vector corresponding to the depth at which there are paleodata information
- Returns
ensembleValuesToPaleo – A matrix of age ensemble on the PaleoData scale
- Return type
array
- pyleoclim.utils.lipdutils.modelNumber(model)[source]
Assign a new or existing model number
- Parameters
model (list) – List of possible model number. Obtained from isModel
- Returns
modelNum – The number of the model
- Return type
int
- pyleoclim.utils.lipdutils.pre_process_list(list_str)[source]
Pre-process a series of strings for capitalized letters, space, and punctuation
- Parameters
list_str (list) – A list of strings from which to strip capitals, spaces, and other characters
- Returns
res – A list of strings with capitalization, spaces, and punctuation removed
- Return type
list
- pyleoclim.utils.lipdutils.pre_process_str(word)[source]
Pre-process a string for capitalized letters, space, and punctuation
- Parameters
string (str) – A string from which to strip capitals, spaces, and other characters
- Returns
res – A string with capitalization, spaces, and punctuation removed
- Return type
str
- pyleoclim.utils.lipdutils.promptForVariable()[source]
Prompt for a specific variable
Ask the user to select the variable they are interested in. Use this function in conjunction with readHeaders() or getTSO()
- Returns
select_var – The index of the variable
- Return type
int
- pyleoclim.utils.lipdutils.queryLinkedEarth(archiveType=[], proxyObsType=[], infVarType=[], sensorGenus=[], sensorSpecies=[], interpName=[], interpDetail=[], ageUnits=[], ageBound=[], ageBoundType=[], recordLength=[], resolution=[], lat=[], lon=[], alt=[], print_response=True, download_lipd=True, download_folder='default')[source]
This function allows to query the LinkedEarth wiki for records.
This function allows to query the LinkedEarth wiki for specific catagories. If you have more than one keyword per catagory, enter them in a list. If you don’t wish to use a particular terms, leave a blank in-between the brackets.
- Parameters
archiveType (list of strings) – The type of archive (enter all query terms, separated by a comma)
proxyObsType (list of strings) – The type of proxy observation (enter all query terms, separated by a comma)
infVarType (list of strings) – The type of inferred variable (enter all query terms, separated by a comma)
sensorGenus (list of strings) – The Genus of the sensor (enter all query terms, separated by a comma)
sensorSpecies (list of strings) – The Species of the sensor (enter all query terms, separated by a comma)
interpName (list of strings) – The name of the interpretation (enter all query terms, separated by a comma)
interpDetail (list of strings) – The detail of the interpretation (enter all query terms, separated by a comma)
ageUnits (list of strings) – The units of in which the age (year) is expressed in. Warning: Separate each query if need to run across multiple age queries (i.e., yr B.P. vs kyr B.P.). If the units are different but the meaning is the same (e.g., yr B.P. vs yr BP, enter all search terms separated by a comma).
ageBound (list of floats) – Enter the minimum and maximum age value to search for. Warning: You MUST enter a minimum AND maximum value. If you wish to perform a query such as “all ages before 2000 A.D.”, enter a minimum value of -99999 to cover all bases.
ageBoundType (list of strings) – The type of querying to perform. Possible values include: “any”, “entire”, and “entirely”. - any: Overlap any portions of matching datasets (default) - entirely: are entirely overlapped by matching datasets - entire: overlap entire matching datasets but dataset can be shorter than the bounds
recordLength (list of floats) – The minimum length the record needs to have while matching the ageBound criteria. For instance, “look for all records between 3000 and 6000 year BP with a record length of at least 1500 year”.
resolution (list of floats) – The maximum resolution of the resord. Resolution has the same units as age/year. For instance, “look for all records with a resolution of at least 100 years”. Warning: Resolution applies to specific variables rather than an entire dataset. Imagine the case where some measurements are made every cm while others are made every 5cm. If you require a specific variable to have the needed resolution, make sure that either the proxyObservationType, inferredVariableType, and/or Interpretation fields are completed.
lat (list of floats) – The minimum and maximum latitude. South is expressed with negative numbers. Warning: You MUST enter a minimum AND maximum value. If you wish to perform a query looking for records from the Northern Hemisphere, enter [0,90].
lon (list of floats) – The minimum and maximum longitude. West is expressed with negative numbers. Warning: You MUST enter a minimum AND a maximum value. If you wish to perform a query looking for records from the Western Hemisphere, enter [-180,0].
alt (list of floats) – The minimum and maximum altitude. Depth below sea level is expressed as negative numbers. Warning: You MUST enter a minimum AND a maximum value. If you wish to perform a query looking for records below a certain depth (e.g., 500), enter [-99999,-500].
print_response (bool) – If True, prints the URLs to the matching LiPD files
download_lipd (bool) – If True, download the matching LiPD files
download_folder (string) – Location to download the LiPD files. If “default”, will download in the current directory.
- Returns
res
- Return type
the response to the query
- pyleoclim.utils.lipdutils.searchVar(timeseries_list, key, exact=True, override=True)[source]
This function searched for keywords (exact match) for a variable
- Parameters
timeseries_list (list) – A list of available series
key (list) – A list of keys to search
exact (bool) – if True, looks for an exact match.
override (bool) – if True, override the exact match if no match is found
- Returns
match – A list of keys for the timeseries that match the selection criteria.
- Return type
list
- pyleoclim.utils.lipdutils.similar_string(list_str, search)[source]
Returns a list of indices for strings with similar values
- Parameters
list_str (list) – A list of strings
search (str) – A keyword search
- Returns
indices – A list of indices with similar value as the keyword
- Return type
list
- pyleoclim.utils.lipdutils.timeUnitsCheck(units)[source]
This function attempts to make sense of the time units by checking for equivalence
- Parameters
units (string) – The units string for the timeseries
- Returns
unit_group – Whether the units belongs to age_units, kage_units, year_units, ma_units, or undefined
- Return type
string
- pyleoclim.utils.lipdutils.whatArchives(print_response=True)[source]
Get the names for ArchiveType from LinkedEarth Ontology
- Parameters
print_response (bool) – Whether to print the results on the console. Default is True
- Returns
res
- Return type
JSON-object with the request from LinkedEarth wiki api
- pyleoclim.utils.lipdutils.whatInferredVariables(print_response=True)[source]
Get the names for InferredVariables from LinkedEarth Ontology
- Parameters
print_response (bool) – Whether to print the results on the console. Default is True
- Returns
res
- Return type
JSON-object with the request from LinkedEarth wiki api
- pyleoclim.utils.lipdutils.whatInterpretations(print_response=True)[source]
Get the names for interpretations from LinkedEarth Ontology
- Parameters
print_response (bool) – Whether to print the results on the console. Default is True
- Returns
res
- Return type
JSON-object with the request from LinkedEarth wiki api
- pyleoclim.utils.lipdutils.whatProxyObservations(print_response=True)[source]
Get the names for ProxyObservations from LinkedEarth Ontology
- Parameters
print_response (bool) – Whether to print the results on the console. Default is True
- Returns
res
- Return type
JSON-object with the request from LinkedEarth wiki api
- pyleoclim.utils.lipdutils.whatProxySensors(print_response=True)[source]
Get the names for ProxySensors from LinkedEarth Ontology
- Parameters
print_response (bool) – Whether to print the results on the console. Default is True
- Returns
res
- Return type
JSON-object with the request from LinkedEarth wiki api
- pyleoclim.utils.lipdutils.whichEnsemble(ensembleTableList)[source]
Select an ensemble table from a list
Use in conjunction with the function isMeasurement
- Parameters
measurementTableList (list) – List of measurement tables contained in the LiPD file. Output from the isMeasurement function
csv_list (list) – Dictionary of available csv
- Returns
csvName – the name of the csv file
- Return type
string
- pyleoclim.utils.lipdutils.whichMeasurement(measurementTableList)[source]
Select a measurement table from a list
Use in conjunction with the function isMeasurement
- Parameters
measurementTableList (list) – List of measurement tables contained in the LiPD file. Output from the isMeasurement function
- Returns
csvName – the name of the csv file
- Return type
string
jsonutils
This module converts Pyleoclim objects to and from JSON files.
Useful for obtaining a human-readable output and keeping the results of an analysis. The JSON file can also be used to swap analysis results between programming languages.
These utilities are maintained on an as-needed basis and that not all objects are currently available.
- pyleoclim.utils.jsonutils.PyleoObj_to_dict(obj)[source]
Transform a pyleoclim object into a dictionary.
The transformation ensures that all the objects are JSON serializable (i.e. all numpy arrays have been converted to lists.)
- Parameters
obj (pyleoclim.core.io) – A pyleoclim object from the UI module
- Returns
s – A JSON-encodable dictionary
- Return type
dict
See also
pyleoclim.utils.jsonutils.isPyleoclim
Whether an object is a valid Pyleoclim object
- pyleoclim.utils.jsonutils.PyleoObj_to_json(obj, filename)[source]
Serializes a Pyleoclim object into a JSON file
- Parameters
obj (pyleoclim.core.ui) – A Pyleoclim object from the UI module
filename (str) – Filename or path to save the JSON to.
- Return type
None
See also
pyleoclim.utils.jsonutils.PyleoObj_to_dict
Encodes a Pyleoclim UI object into a dictionary that is JSON serializable
- pyleoclim.utils.jsonutils.isPyleoclim(obj)[source]
Check whether an object is a valid type for Pyleoclim ui object
- Parameters
obj (pyleoclim.core.ui) – Object from the Pyleoclim UI module
- Returns
Bool
- Return type
{True,False}
- pyleoclim.utils.jsonutils.iterate_through_dict(dictionary, objname)[source]
Iterate through the keys of a json file to correctly identify nested Pyleoclim objects and instantiate them
- Parameters
dictionary (dict) – Dictionary obtained from the JSON file
objname (str) – The desired Pyleoclim object
- Returns
a – A dictionary containing the right key-value type for the object
- Return type
dict
- pyleoclim.utils.jsonutils.json_to_PyleoObj(filename, objname)[source]
Reads a JSON serialized file into a Pyleoclim object
- Parameters
filename (str) – The filename/path/URL of the JSON-serialized object
objname (str) – Name of the object (e.g., Series, Scalogram, MultipleSeries…)
- Returns
pyleoObj – A Pyleoclim UI object
- Return type
pyleoclim.core.ui
See also
pyleoclim.utils.jsonutils.open_json
open a json file from a local source or URL
pyleoclim.utils.jsonutils.objname_to_obj
create a valid Pyleoclim object from a string
- pyleoclim.utils.jsonutils.objname_to_obj(objname)[source]
Returns the correct obj type for the name of a Pyleoclim UI object
- Parameters
objname (str) – Name of the object (e.g., Series, Scalogram, MultipleSeries…)
- Raises
ValueError – If the name of the object is not valid
- Returns
obj – A valid Pyleoclim object for the UI module
- Return type
pyleoclim.core.ui